As stated many times above, we call this an unjust enrichment. I have seen this many times before in my line of work, a customer trying to state they "thought they won the lottery" or they "thought a family member knew of their financial needs and provided."
The bank can and will find the error and they will correct it, whether in your favor or not.
I hope you have made the right decision to notify the bank of your unjust enrichment. If you're not careful you could be held legally responsible for the monies owed back should you spend it. Be very careful when you take something that is not yours. To even hear someone ask that question, fully aware the money is not his/hers, is revolting.
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"For with God NOTHING shall be impossible."