Replacement of sins with good

You are correct. Such a doctrine does not exist. Because in Christian theology Good Deeds cannot account for or replace Bad Deeds.

There is of course differences in the Christian community regarding the idea of “salvation” and what must be done to obtain it.

This is commonly argued amongst Christians as the debate between salvation by grace and salvation by works. But in fact it is probably safe to say most Christians believe that salvation is by grace and the result is the works (good deeds).

So Christians do not believe one can do 10 good things and 9 bad things and still hope to goto heaven. Or one cannot Do one bad thing and 2 good things and expect to goto heaven. Christians believe that after one “repents” ... then the individuals heart is changed. And they are no longer able to sin. And sin falls away in their life. Then all their deeds become “good” by Grace of God. Naturally. Not because they intended them to be good. But because they acted out of a truly good heart... their actions are seen as Good. Though they did not necessarily think beforehand about it. They just acted and said and did what they felt was good in their hearts. These people don’t turn around and do bad things later On. They have repented already. They stopped having an evil heart. Because they know now it is wrong. And their bad deeds have become good deeds. Because God has replaced their evil deeds with good.

If you don’t know what an evil heart is, then you cannot repent of it. Then how will you ever know if your deeds are good or bad?

The closest equivalence would be that God does not remember the person's sins anymore for someone who truly repents. This has started even under the Mosaic (Old) Covenant and of course continuing under the New Jesus Covenant. Clean slate.

Below are some OT references showing how God offered this "forgive" and "forget" to 1) Israel as a whole, 2) an Israelite King, and 3) an Israelite.

1. To Israel as a whole, verse 25 of Isa 43:22-25 : God is sad why Israel wouldn't come to Him for forgiveness and restoration after God punished them by exiling them to Babylon.
2. To King Hezekiah, verse 17 of Isa 38:15-20 : Hezekiah praised God after God promised to heal him.
3. To an Israelite, verse 12 of Ps 103:8-18 : The LORD is merciful and compassionate to the children who fear him.

You can see how repentance (plus possibly the system of temple sacrifices) enables an Israelite to be restored back to covenant righteousness, and God would forget his/her sin. The forgiving / forgetting happened even in this life, no need to wait until death! But GOD KNEW how it was still not good enough, because as we read in the OT, Israel kept sinning and sinning again. Therefore after exile (the biggest punishment to Israel so far), God announced His plan to give them a new heart that doesn't sin so that God didn't have to punish them AGAIN to that extent (Eze 11:19; Eze 36:26; Jer 31:31–34).

That's where Jesus came in: as a fulfillment of that promised plan. For those who accepted Jesus as Lord and Savior, Jesus cancels completely the curse caused by Adam's sin (the original sin), another forgetting (!) (recapitulation theory). He also frees us from the power of sin, so it should be easier for us NOT to sin (ransom theory). Most importantly, another work of Jesus is to give the believer this promised NEW HEART which Jesus starts "installing" through the ministry of the Holy Spirit. As long as we don't "uninstall" / abuse it but instead cooperate with the Holy Spirit's work to purify us, the believer will no longer sin. But it's inevitable that even a sincere believer will trip up and falls into temptation now and then, but GOD KNOWS THAT! Since our own being is now a temple (because the Holy Spirit resides in us), all we need to do is to genuinely repent and ask Jesus, our priest, to intercede for us, asking forgiveness from God. Then God will again forget our sins! So that's a LOT to be thankful for. Therefore, if we truly appreciate this we should then be VERY CAREFUL, out of RESPECT, GRATITUDE, and FEAR OF HURTING GOD, to try our best not to fall into temptation again (moral influence theory).

In my opinion, if God is very gracious to forget our sins in THIS life, both under the Old Mosaic covenant and under the New Jesus covenant, wouldn't you think God will do the same AFTER death? There are solid Biblical support for this which I don't have to go into.

Christians would NOT normally phrase this forgetting / forgiving sin as REPLACING bad deeds with good deeds, but phrase it as God's restoring believers into the state of righteousness under the covenant God made with us. To me, the various theories of atonement you referenced in your question (substitutionary, ransom, recapitulation, and moral influence) are different aids to EXPLAIN how Jesus's sacrifice enables God to restore us to be righteous again in order for us to have flourishing life just as Israel was blessed in the promised land as long as they don't break the covenant. As C.S. Lewis said, we do not need to believe any ONE theory of atonement. In fact, in Adam Johnson's book titled Atonement: A Guide for the Perplexed, he suggests we use all of the theories because atonement is simply too rich to be confined to a single model.

What's important is we do our part so God can do His part to save us. When we TAKE THE OFFER and stay steadfast through the rest of our lives ABIDING within the covenant, we will then eligible to finally enter his Kingdom at the end of time.

Bible reference source: Does God really forget our sins?

ADDENDUM

I find a very loose translation of the passage surrounding verse 70 here:

[Quran 25:63] The worshipers of the Most Gracious are those who tread the earth gently, and when the ignorant speak to them, they only utter peace.

[Quran 25:64] In the privacy of the night, they meditate on their Lord, and fall prostrate.

[Quran 25:65] And they say, "Our Lord, spare us the agony of Hell; its retribution is horrendous."

[Quran 25:66] "It is the worst abode; the worst destiny."

[Quran 25:67] When they give, they are neither extravagant nor stingy; they give in moderation.

[Quran 25:68] They never implore beside God any other god, nor do they kill anyone - for God has made life sacred - except in the course of justice. Nor do they commit adultery. Those who commit these offenses will have to pay.

[Quran 25:69] Retribution is doubled for them on the Day of Resurrection, and they abide therein humiliated.

[Quran 25:70] Exempted are those who repent, believe, and lead a righteous life. God transforms their sins into credits. God is Forgiver, Most Merciful.

[Quran 25:71] Those who repent and lead a righteous life, God redeems them; a complete redemption.

[Quran 25:72] They do not bear false witness. When they encounter vain talk, they ignore it.

[Quran 25:73] When reminded of their Lord's revelations, they never react to them as if they were deaf and blind.

[Quran 25:74] And they say, "Our Lord, let our spouses and children be a source of joy for us, and keep us in the forefront of the righteous."

[Quran 25:75] These are the ones who attain Paradise in return for their steadfastness; they are received therein with joyous greetings and peace.

[Quran 25:76] Eternally they abide therein; what a beautiful destiny; what a beautiful abode.

[Quran 25:77] Say, "You attain value at my Lord only through your worship. But if you disbelieve, you incur the inevitable consequences."

When verse 70 is read in context (verses 63 to 77), the similarity to God forgetting sins is quite striking. The passage reads like a Psalm / Proverb, emphasizing how those who repent, believe, and lead righteous life will receive mercy from God while those who don't will receive double punishment (verse 69). So maybe verse 70 is a poetic way to reverse verse 69 saying that instead of DOUBLE punishment, the righteous will INSTEAD receive credits to be applied to their minus account resulting in ZERO BALANCE. The spirit of the passage of the whole emphasizes complete redemption (esp verse 71), so just like in Christianity where the theory of atonement you prefer doesn't matter, maybe the manner in which God applies mercy to us also doesn't matter much.

The Muslim belief that God will replace evil deeds with good merits/deeds is not based on Christianity. Yes, the Bible says that God is merciful and forgiving, but nowhere does it suggest that after death God will replace sinful deeds with good deeds on judgement day.

The basic difference between Islam and Christianity (as I understand it from a Protestant perspective) is that Muslims do not believe they need a saviour because Islam teaches that man is born sinless and does not have a sin nature from which he needs to be saved. Sura 11:114 suggests that Muslims can cancel out bad deeds by good deeds. Yes, Muslims believe they must repent of sin and that they can seek forgiveness from Allah, but the Christian belief that payment for sin is required by God and that only Christ Jesus can atone for our sins is anathema to Islam. They do not recognise the need for a saviour to free them from the penalty of sin. Here are a few Bible verses on the subject of sin, repentance and God’s righteous judgement:

“For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life” (John 3:16).

“Whoever believes in the Son has eternal life, but whoever rejects the Son will not see life, for God’s wrath remains on him” (John 3:36).

Jesus says, "Therefore I said to you that you will die in your sins; for unless you believe that I am He, you will die in your sins" (John 8:24).

“For by works of the law no human being will be justified in [God’s] sight, since through the law comes knowledge of sin. But now the righteousness of God has been manifested apart from the law, although the Law and the Prophets bear witness to it—the righteousness of God through faith in Jesus Christ for all who believe” (Romans 3:20–22a).

“For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord” (Romans 6:23).

“Therefore, there is now no condemnation for those who are in Christ Jesus, because through Christ Jesus the law of the Spirit of life set me free from the law of sin and death... Those controlled by the sinful nature cannot please God” (Romans 8:1, 2 and 8).

“For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, not a result of works, so that no one may boast” (Ephesians 2:8-9).

The Protestant view is that we are judged on whether we accepted or rejected Christ Jesus as our saviour while we lived. After we die, it’s too late. The doctrine is summed up this way:

“Just as people are destined to die once, and after that to face judgment, so Christ was sacrificed once to take away the sins of many; and he will appear a second time, not to bear sin, but to bring salvation to those who are waiting for him” (Hebrews 9:27–28).

Islam rejects the Christian view of our inherited sin nature and the need for Christ Jesus to atone for our sins by himself paying the penalty in order to satisfy God’s holiness and justice. That is why you will never find any biblical basis for the Islamic view that God will replace our sinful deeds with good deeds on the day of Judgement.