It looks like there are records for the gun so a letter will tell you the date it shipped but I am not sure what other information you may find. It is a Remington gun and the IBM cards they used don't provide the same information as the written record Parker Bros.'s books would? We know it is a 12 gauge with 32 inch barrel and a pistol grip stock. Gold inlays.....? A letter may tell you but the odds are against you I suspect.
Join the PGCA and get a letter for $40.00, that is the cheapest way. See the main web page at
www.parkerguns.org and click the "Research Letter" link on the left to learn how to obtain one.