$1000? I wouldn't worry about losing this customer. They had to know it wasn't their money. I'd give them 30 days to repay it. If they don't, write it off, close their account, and hand them a 1099-C for the debt forgiven.
Hassling with a repayment plan for a low-balance, less-than-honest customer will be more trouble than it is worth.
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Opinions are mine not my employer's, and should not be taken as legal advice.