A bank asking for screenshots?
Lol, they do

I can't imagine that. A screenshot has no legal value. I can make any screenshot you want on Photoshop.
That's what I told my bank too

It shows banks are dinosaurs when it comes to technology.
Think of it this way: the bank wants to comply with regulation, and wants to spend as little time on this as possible. If it's too much work, they'll prefer to just close your account.
My suggestion is to give them evidence that can easily prove your funds have no criminal origin, so they can close your case.