Like mentioned above, the value will be pretty low - I would think $150 tops IF someone accepts the connection. You must also realize it is not a widely prized or sought after weapon. It’s not a SKS, Mosin, Mauser, MAS-36, TT-33, or anything else military collectors seek out – but you never know with today’s crazy prices. The main value for 'bring backs' it the paperwork. Unfortunately, the proof of provenance between the paperwork and firearm is lacking. The DD Form 603 was supposed to be used for war trophy firearms, but a generic letter like yours was often used. The 603 had a block for serial number, model, caliber, type, etc. that (if filled out) would more directly connect the rifle to the paperwork. Even though your shotgun probably has no S/N, any additional information besides “locally made shotgun” would have been a plus – such as break-barrel, single shot, 28ga, two-piece wood stock and handguard, etc. I know most military clerks would only do the minimum required to get it approved, which hurt the value in situations will like yours.
I vote you keep it in the family…..That will always trump poor provenance. Professionally frame the paperwork so it wont fade and hang it in your house with the shotgun and a pic of your dad in his uniform. Otherwise, find someone else in the family that will appreciate it for what it is and give it to them for future safekeeping. Trust me, someone in your family – whether now, or 30 years from now, will appreciate this piece of family history more than a stranger ever will. Be a good caretaker until you find it a good home with a relative, sibling, or offspring.
TOM