Not to nitpick, but the "stable" part isn't necessarily true. If the money is just being used for a down payment, and not being cited as recurring income, they wouldn't care whether it's stable.
Side note: I still can't make sense of why lenders care about the money's source being legitimate but the title company doesn't, per my experience: https://news.ycombinator.com/item?id=28163885
Wait, was that for a mortgage? I bought a house outright with cash that had been moved from Gemini (US crypto exchange) to Schwab less than two weeks before and the title company never had any questions about it.
Side note: I still can't make sense of why lenders care about the money's source being legitimate but the title company doesn't, per my experience: https://news.ycombinator.com/item?id=28163885