The UCC (3-312) outlines how a claim for a lost, stolen, destroyed instrument can be perfected. Once perfected, the claim is enforceable.
At our institution, we have the claimant complete a "Declaration of Loss" form after which management will review, determine whether the item is still outstanding and then centrally a stop payment is placed on the item to cause it to reject and prevent duplicate payment of the item since a refund has been processed.
While placing a Stop Payment in general is not permitted, this is how to prevent duplicate payment of an item only after the UCC requirements have been met.
The opinions expressed are mine and do not necessarily reflect those of my employer.