A business customer notified the bank about a check fraud by the customer from 10 mos ago and wants the bank to submit a fraud claim. Is it the bank's responsibility to do that?

Thank You

You have given us no information to go on. What do you mean "about a check fraud by the customer"? They did something fraudulent?

There a lot of different types of "check fraud." What exactly happened that was fraudulent?

Whatever the scenario; 10 months later? Too bad, so sad.

That is not an accurate statement as the answer will depend on state law and the deposit agreement. In many states, the statute of limitations in some Uniform Commercial Codes for reporting a forgery is one year. While this may be shortened by account agreement, the OP has not provided enough information to answer their question.