I love this kind of detective work, but you’re taking on a tough case
If there are no indications on the gun of anything special, chances are that the S&W history letter Alan pointed you toward will take you no farther than a distributor or possibly retailer where the factory shipped it. Whether there is any chance to trace it from there (if the place still exists) is highly questionable since you are not law enforcement.
Taking your customer’s story at face value, Mr. Webb may have bought the gun, or he may have received it from someone else and passed it on to his friend the cop because he didn’t need it.
I’m sure you want to get the lady the best price for her gun, but it’s hard to envision that you can gather enough actual evidence that would ethically allow you to try to sell and price this gun based on its Jack Webb association.