The case was made for the German S-Patrone in 1916. H = Rheinische Metallwarenfabrik (in the 1880s, they took over a military contract from Hörder Hütten- und Bergwerksverein, which is where the H on military cases comes from) “S67” identifies this S case as made from brass with 67 percent copper, instead of the usual 72 percent.
The bullet is a hunting bullet in place of the original spitzer bullet.
Designation 8 x 57 J (changed by CIP in 1984 to 8 x 57 I) is a civilian designation, created in 1926 for barrels with a bore diameter of 7.8 mm (.307). German military never had any 7.8 mm bore adopted. Therefore, there is no 8x57 I military weapon.
German military bore diameter was 7.9 mm (.311), starting with Gewehr 88 through 1945. Rifles having the military bore and ammunition could freely be purchased by civilans. This caliber is called 8 x 57 IS by CIP, never by German military.
As a result, rifles with 7.8 mm bore (quite a number even tighter) and the “real-thing” 7.9 mm bore co-existed over decades in Germany.
The hunting bullet of the cartridge shown could be of 8.1 mm (.319) maximum diameter (intended for a 8 x 57 I weapon), provided the case neck was re-formed. If it is 8.2 mm diameter (…323), it is intended for a 8 x 57 IS / military bore 7.9 mm weapon.