Why is speaking about the conventional self in this life ok, but speaking about the conventional self in past and future lives forbidden?

This is a lot to take in and i've tried to read as carefully as i can.

As i understand it, when you say hypostatic you mean something close to 'a background element which is instrumental to knowledge & vision or simply something upon which a person's experience inherently depends, as a soul, an invisible personal element apart from this worldly phenomena, it is transcendental to the world & nature itself.

I don't understand why you assume this;

speaking of the self in other lives in the same continuity is strictly forbidden as always contradicting anatman and necessarily presupposing hypostatic existence.

Isn't this what the Bhikkhus did when speaking of Pukkusati being reborn? Were they not there speaking about a being in a future existence by the name of a previous birthname and were not censored for this? This happens more in the Sutta;

'Venerable sir, Anathapindika the householder is diseased, in pain, severely ill. ...'It would be good if Ven. Sariputta would visit Anathapindika's home, out of sympathy for him.'" ...[so they visit him]... Then Ven. Sariputta and Ven. Ananda, having given this instruction to Anathapindika the householder, got up from their seats and left. Then, not long after they left, Anathapindika the householder died and reappeared in the Tusita heaven. Then Anathapindika the deva's son, in the far extreme of the night, his extreme radiance lighting up the entirety of Jeta's Grove, went to the Blessed One and, on arrival, bowed down to him and stood to one side. As he was standing there, he addressed the Blessed One with this verse:

This blessed Jeta's Grove, home to the community of seers, where there dwells the Dhamma King: the source of rapture for me.

Action, clear-knowing, & mental qualities,[1] virtue, the highest [way of] life: through this are mortals purified, not through clan or wealth.

Thus the wise, seeing their own benefit, investigating the Dhamma appropriately, should purify themselves right there.

As for Sariputta: any monk who has gone beyond, at best can only equal him in discernment, virtue, & calm. That is what Anathapindika the deva's son said. The Teacher approved. Then Anathapindika the deva's son, [knowing,] "The Teacher has approved of me," bowed down to him, circled him three times, keeping him to his right, and then disappeared right there.

Then when the night had past, The Blessed One addressed the monks: "Last night, monks, a certain deva's son in the far extreme of the night, his extreme radiance lighting up the entirety of Jeta's Grove, came to me and, on arrival, bowed down to me and stood to one side. As he was standing there, he addressed me with this verse:

This blessed Jeta's Grove, home to the community of seers, where there dwells the Dhamma King: the source of rapture for me.

Action, clear-knowing, & mental qualities, virtue, the highest [way of] life: through this are mortals purified, not through clan or wealth.

Thus the wise, seeing their own benefit, investigating the Dhamma appropriately, should purify themselves right there.

As for Sariputta: any monk who has gone beyond, at best can only equal him in discernment, virtue, & calm. "That is what the deva's son said. And [thinking], 'The Teacher has approved of me,' he bowed down to me, circled me three times, and then disappeared right there."

When this was said, Ven. Ananda said to the Blessed One, "Lord, that must have been Anathapindika the deva's son. Anathapindika the householder had supreme confidence in Ven. Sariputta."

"Very good, Ananda. Very good, to the extent that you have deduced what can be arrived at through logic. That was Anathapindika the deva's son, and no one else." https://www.accesstoinsight.org/tipitaka/mn/mn.143.than.html

I think think is close as they refer to a certain 'Deva's son' as Anathapindika. Maybe you can clarify the controversy for me and tell whether i am close with hypostatic meaning.

I must read the entire question later. However, to answer the title of the question: the Pali suttas have a number of examples of speaking about the 'conventional self' in past and future lives (eg. MN 81, MN 123 and MN 143).

Personally, I regard all of this as "fake dhamma" composed under the ambitions of King Ashoka, when probably the Jataka, Buddhavamsa and Apadana (which are all about literal past lives) were composed. For example:

• MN 81 (which says "I was" in a past life) contradicts SN 22.79 (which says any recollect of the past is not-self and mere aggregates).
• MN 81 includes the phrase 'ahaṃ tena samayena') found numerously in the later day Buddhavamsa.
• MN 123 (where a new born infant says "I am") contradicts MN 64 (which says a new born infant cannot have "identity").
• MN 143 contradicts other suttas that say Anathapindikovada was a stream-enterer. If Anathapindikovada was a stream-enterer, he obviously understood the dhamma of non-attachment spoken in MN 143, which MN 143 says Anathapindikovada never heard before.

It is both from chronological point of view and as a class of poetical composition, [that] the Pali Apadāna ranks with the Buddhavaṁsa and Cariyāpiṭaka. According to the traditional enumeration of the Buddhist canonical texts, these are reckoned as the last three works of the Khuddaka Nikāya. Even from the doctrinal point of view the three works together show the Mahāyāna [OMG!] Buddhism in the making.

Buddhakhetta and Buddhāpadāna by Mr. Dwijendralal Barua, M.A