Ecash TIDES using Cashu and Stratum v2

Ok so if an ehash is sent to another person before redemption would the pool/mint need to update the share log to keep track of the swap?

I think I understand how this would work now for an ehash to be paid multiple times: when an ehash is redeemed the share is looked up in the share log, if the share is still in the share window then a new ehash is provided. If the ehash falls out of the share window, then it can no longer be redeemed. Is my understanding correct?