Unique Identifier.
When I was in the insurance business, I would tell my clients to add a mark somewhere on the gun that only they could have made.
Take off the grip and make three small scratches on the frame, something like that.
Take eight or ten pictures of each gun and include their identifiers.
Save it to a file and send the file to your Mom and your agent.
Make sure your coverage has a firearm endorsement beyond normal limits if you need it. It is not expensive and worth it if you are a collector.
Talk to your agent about replacement cost versus cash value.