Fish and Game will most likely run it with the ATF to see who the last known purchaser was (if it was made after 1968 it will have a serial number). Response from the ATF for found weapons inquiries take a week or two for a response. Just depends on how much work the F&G is willing to put toward finding the owner. When I was working for a Sheriff's Office, I ran to ground several found weapons owners. Sometimes it takes a little extra digging and following the purchase line.