Just got an account that was opened with a fake ID. The problem is that they deposited cash into this account and I don't know what I should do with the cash if I closed the account. The money belongs to them since they deposited it but they did it under someone else's name. Does anybody else have a solution besides putting the account on hold and requiring them to give us a valid ID before they can access the accounts funds?

A fake ID or someone else's ID?

I'm just asking (and i'm not a deposit compliance person at all)....but if deposited with "John Smith's" ID and John Smith is a real person (just not the person sitting in front of you), then my suspicion would be that not only the ID is John Smith's, but maybe the money too.

It's a fake ID. The photo is of the person that walked in but the name along with the address if someone else's. The two don't match.

Sounds like identity theft. What does your Red Flag policy say you should do?
Contact your local Law Enforcement. See if they can advise you on how to proceed. Depending on dollar amount look at filing a SAR.

I recommend freezing the account and not allowing anything to go in or out.

I would argue that the thief gave up ownership of the cash when they deposited it into an account titled to another person.

Put the account on hold, but do not ask them for a valid ID- that does not fix the problem. If they actually show up to complete a transaction, have the branch call the local police while the thief is present.