"capture papers" are the US Army paperwork listing the gun, and authorizing the solider to keep it, and bring it home as a war trophy. They range from an official form to a hand written receipt, and may or may not identify the gun by serial number, though most do.
They are much more rare than the guns themselves. Reason #1, lots of the guns were never officially papered, #2 of the ones that were, often the paperwork has been lost over the years.
I have an ac 43, in good, but not quite as good finish condition as the OP's gun. Mine was a commercial import, after the war, and has the importer's stamp on it. Bought it about a decade ago for $350.
IF you are going to shoot it (and shooting it will not hurt it) DO NOT USE +p ammo, of ANY kind. The gun was built to run on 115gr FMJ (at a nominal 1150fps) and will last a long time if you stay away from +p stuff.
Oh, and be aware, the P.38 ejects TO THE LEFT!!!!
(something I had never been aware of, until I got one!) Now, its my favorite piece to shoot on the range when a kid in the next lane pelts me with brass, I get out the P.38, and fling some back!
(not entirely a joke,
)
Also, be aware that the proper, period correct Nazi marked holster (in good condition) ADDs up to several hundred dollars to the collector value.
If there are any "bringback" papers make copies, to keep with the gun, and put the originals in a safe place.
Nice piece of history, and family history, keep it well, and enjoy!