In common law countries, there is an extensive body of law about lost, mislaid, and abandoned property and how to deal with them. Lost, mislaid and abandoned are technically distinct classifications. Lost is a wallet on the side of the road. Mislaid is a wallet left on the counter at a store. Abandoned is something that was intentionally thrown away.

Abandoned property is basically finders keepers. Mislaid property should be left and the owner contacted, and the proprietor where it was left notified to help effect that. Lost property where the owner is known must also be returned. Lost or mislaid property might eventually be claimed when the return is impossible, for example, one cannot identify or contact owner after a long period, including perhaps posting public notices. At that point, it becomes considered abandoned.

Specifics vary a bit by jurisdiction, but I don't see it likely ever applying when you know who it came from and it's all on record. No reasonable person abandons cash in the wrong account. It is clearly mislaid. Maybe if they don't respond despite repeated formal contacts via legal channels. Obviously something to consult with a lawyer about over these kind of stakes...