It's quite possible it is a war trophy. If there is no import stamps it's about certain it's a war trophy. Either liberated by your grandfather or someone else.
As TRAP mentioned, in 1905 the German military changed their groove diameter to .323 from .318 and adopted the spitzer bullet. Now, admittedly military rifles are not my thing however, one cannot spend much time studying German firearms without gaining at least some familiarity if by no other means than osmosis. I have read multiple times by reputable sources that to make the pre-1905 rifles compatible with the new groove diameter German armorers merely enlarged the throat of the early rifles, thus guaranteeing enough room for bullet release. One revolution of the bullet in the bore and it was resized and the larger throat took care of any pressure difference.
As I understand it, American 8 X 57 ammo has always been loaded with .321 bullets and, it's a fact it is loaded to much lower pressure than its European counterpart. IF your gunsmith gives the rifle a clean bill of health I would think American loaded ammo would be fine.
Now, I'm positive someone, somewhere, is going to tell how many thousands of rounds of hot, .323, machine gun ammo they've fired in their old, .318 bored rifle without a hitch. All I can say is good for them.
There are 8 rounds missing from the box, so I assume he shot them in this gun at some time.
