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You have a previous refusal wherein you did not disclose relevant information and (presumably) you did not get caught. You want to make a fresh application.
Can I declare that account in my new visa application and explain where that money has come from?
Yes of course, documenting irregular account flows is part of 'best practices' advice. Otherwise they will worry if they see unprovenanced funds movement. In the argot of this site, the term 'funds parking' is used to describe how it works...
How can I explain why I didn't declare that account before?
Good question! In the last pages of the application form there is a section for free-form text. You can put your explanation there.
Having said that, the very last thing you want to do is to enter your explanation as you go along. It should be carefully hammered out beforehand using Notepad or similar composition tool. This can take a while and might involve several draft copies. We see a lot of serial refusals that could have been avoided by skillful wordsmithery; it's part of why solicitors can be expensive.
To give you an idea about expectations, it is not uncommon for a good solicitor to spend a whole afternoon drafting and then another half-day in peer review and another half-day in partner review. This is the sort of exculpatory text that ECO's like and can readily accept. One paragraph, two at the very max.
Avoid insipid expressions of remorse or apologies. This goes in to the more generic category of insulting their intelligence, and they do not appreciate it. If, as you wrote, you were trying to avoid transparency, you can explain it like that.
Another important thing about your explanation: don't try to double down, doing that can change a simple thing into a really awkward thing.