Answer:
If the transactions involved were fraudulent ACH credits followed by fraudulent debit card transactions (purchases or ATM withdrawals), and your customer has filed claims on the fraudulent debits, you have to investigate the customer's claim. If you confirm through your investigation that the ACH credits (which I assume your customer said he didn't recognize) and the debit card transactions were fraudulent, you have an effective "wash" result. Check the account carefully to ensure that no fees resulted from any of the unauthorized transactions, report the results of your investigation, and you can close the investigation. If it helps make the file complete, you can reverse the credits and debits on the account caused by the fraudulent transactions, which will net to $0 both in the account and in your fraud charge-offs account.
It appears your customer's account has been compromised. To reduce the odds of the account's being further compromised in larger amounts (which are likely not to balance for a zero dollar loss), you should close the account out and open another.
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