Look at the language in the signature card the customer signed. If it's of recent vintage, it should say that your bank has the right to unilaterally close the account. Cite that language in your letter. You are not required to give a reason, but if you do it in close proximity to the attempt to deposit a fraudulent item they should be able to connect the dots.
If the account is receiving federal benefit payments, you are required to give 30 days advance notice. If payroll or any other periodic payment is coming into the account, I encourage you to give notice equal to the intervals between deposits; e.g. if they are paid every two weeks, give them two weeks notice.
Tell them the only over the counter deposits you will accept will be cash and that they should only deposit enough to cover outstanding checks they have already written.
By the way, congratulations. There are a lot of folks who would wait until they actually lost money before it would have occurred to them to close the account.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.