The stop payment in this case is only a tool designed to call the presentation of the original check to your attention so that you don't pay it if you don't have to.
If that declaration of loss is accompanied by a claim from the remitter or payee of the check, what you do depends on how old the check is.
If the check is less than 90 days old, and if it's presented for payment by a holder in due course, you have to honor the check and you will notify the claimant that you cannot honor the claim because the check's been paid.
If the check is 90 or more days old, and you have already honored the claim, you are not obligated to pay the check. You should return it unpaid, return reason "X", with the face of the check clearly marked "Claim paid under UCC 3-312" [4-406 in New York]. The claimant is now obligated to pay the amount of the check to the person with rights of a holder in due course. The bank is off the hook.
Caution: Do not accept an affidavit of loss or claim under UCC 3-312 if you believe that it's actually a case of buyer's remorse or an attempt to recover funds the remitter lost to a fraud or other scheme. And don't accept such an affidavit or claim from anyone other than the remitter/purchaser or payee in the case of a cashier's or teller's check or the issuer or payee in the case of a certified check.