By talking about it to them multiple times she’s covered in case of an investigation. Actually in many ways she WANTS an investigation, then they’ll find the error, and she can give the money back and the whole incident gets to end. The main reason to move it is to separate it logistically, this is her usage account, she does her normal banking out of there. Leaving the money in there is asking for confusion. And since the law says the bank has years to find their error might as well move it someplace that draws interest, get a little benefit from this massive inconvenience.
I can only tell you from experience, working at a bank for many years, that you don't even want to open the door to suspicion in these cases. As is, they will eventually just make an account correction. If she moves the money, she opens the door to all kinds of complications and problems.
While not a legal expert on the matter, this sort of thing is not uncommon because I've seen it as a drive through teller all the way through commercial lender. At least when I used to work in the industry, large deposits were accidentally made into wrong accounts all the time, and never, ever have I heard of a case of the bank or some company eating the loss. Normally the error is discovered quickly and the account will be debited the funds. If the money is no longer there, bank security gets involved. If it is a large amount of money, law enforcement gets tangled up in it. The ones that I recall taking a long time to clear up were international wire transfers.
If she notified the bank, has records of it, does not spend the money and can produce it on demand, it is very possible she would be in the clear. I would not be so sure of that though and it opens the door to suspicion and wrongful, time consuming investigations. You never want to even put yourself in a situation where authorities are suspicious of you. I think bank and law enforcement bureaucracy can get off on the wrong track, refuse to admit they are wrong, and really harass someone who got themselves in a situation like this.
Having seen it for myself, it is actually rather surprising how inaccurate proof departments can be sometimes. I remember being surprised that if no cash was involved, we tellers didn't even have to care if the checks matched the total on the deposit slips. And interesting enough, even if you claimed up to 10 dollars more on the slip than the checks actually added up to - the bank didn't care and would give you the money because it wasn't worth their time to make the correction. I used to wonder if people ever realized this, would they make a tiny deposit every single day and claim the deposit to be 10 dollars more than it really was. Seems like a small amount, but over a year I guess it could add up to fair chunk of change.