An Allianz OneTrip Premiere trip insurance covers $2000 for loss or theft of baggage and personal effects. They reported the loss to airport security. Getting a written notice of that report ought to be enough to file a claim.
If you later recover an item that you've successfully claimed an insurance claim against, you would just have to hand over the item to your insurance company (who might not even want it at that point). And you should have been able to successfully claim the laptop since at the airport, it was most definitely lost and/or stolen.
Also, how can you even assess that the laptop has no physical damage? They can't boot into the OS and can't see that the laptop is in fact completely physically intact. What if the other party broke the webcam or one of the USB ports?
This entirely misses the point. Using travel insurance for "loss or theft" of something when something is actually, well, lost. The guy has possession of his property, how has anything been "lost"?
I really, really doubt a travel insurance company would pay out on this one.
The computer was “lost” for a whole month before being found and 2 months before being returned. You should claim losses immediately anyway so probably he could have gotten the refund before even knowing it was found.