I reluctantly decided to post, even though you and most other Forum members know that I know very little about 7.9x57!
So here goes!!! This is a VERY STRANGE cartridge for a lot of reasons. First, the case is brass. As far as I can tell, by 1943 brass was scarce enough that it’s use on 9mmP08 was strictly limited. it was usually found in non-military 50 round boxes, which I strongly suspect was reserved for senior SS officers who liked to carry Luger pistols which, because of the stepped chamber did not handle steel case ammunition well. There are a few Army type 16 round boxes with brass case ammo made by Geco in '43 & '44, but only three case lots in '43 and one case lot in '44. Again, this was probably for senior officers who preferred the Luger pistol.
One obvious question is, who was making brass case 7.9mm in '43 and why? I seem to remember that the Luftwaffe used brass case ammunition in some guns because it was more reliable in cold weather, but I don’t know who made this ammunition, or exactly why.
Could this original cartridge, which apparently was an SmK load with a Nickel bullet (Sounds like a Czech load to me), have been intended for aircraft use with a foreign (probably Czech) machine gun???
The box leads me in this direction. I have no idea what an “M31” load is, but the powder appears to be dated 1931 (or 1937) and the primer is apparently a 1923 design. The Czechs had a ZB30 light MG which was used in quantity by the SS and perhaps this ammunition was intended for that weapon.This weapon was also produced in Romania and used during the war so this may have been for them. This weapon was used on some Czech aircraft like the Aero A.304, some of which was captured and used by the Luftwaffe. A bomber version, the A.300 and the earlier A.100 also used this MG and were used by the Slovak AF until 1945.
Your box reminds me of a 9x19mm box I have that is by dou in 1943 but uses a Czech powder, not the German powder. It seems very likely this was made for the ZK383 Brno submachine guns used by the SS, the Slovak police and Romania during the war. Details at the link below.
The box is also interesting because of the marking in the lower left corner. I understand these identify the printer of the label. The "c"with an inverted “^” over it is not typically German! When I checked, it turns out to be a character in the Czech alphabet!
I looked for a M31 Machine gun in 7.9mm but couldn’t fine anything.
Bottom line! I have no idea what you have, either the cartridge or the box, which I agree probably goes with the headstamp you illustrate. This would be a good question to post in the Czech Bulletin. I would be happy to post it for you!