Pierrejean & Schneider - I’m sorry but the rim of the empty case shown appears to be to thick to be an 9mm Nambu, and the extractor groove and extractor groove bevel appear to be too wide and the wrong shape. The head, rim and bevel look very much like Belgian manufacture 7.65 mm Parabellum, some of which have the stab-type neck crimps and so of which do not. It is also similar to Austrian cases. There are many variations of unheadstmaped 7.65 mm Para a few of which have the stab crimps. Stab crimps, overall, are common on bottle-neck auto pistol cartridges, not just the 8 mm Nambu.
I have over forty variations of the 8mm Nambu cartridge in my collection, and none have a rim and extractor groove and bevel like the round in the photo. Further, although one cannot say with any certainly from such a picture, the base diameter of the cartridge appears to be the same as the .30 Mauser case next to it, correct for a 7.65 Para cartridge. The 8 mm Nambu is considerable larger in diameter than the standard Mauser/Borchardt/Mannlicher 10 mm head.
.30 Luger, measured from one headstamped AEP specimen:
Rim: 0.391" (9.66 mm)
Base: 0.386" (9.81 mm)
8 mm Nambu, measured from one unheadstamped original Japanese Service cartridge:
Rim: 0.412" (10.46 mm)
Base: 0.4065" (10.33 mm)
I suggest to Schneider that the head (rim) and base be measured to determine which caliber it is. As to who and when, impossible to say without a box label, in my opinion. It looks Belgian to me in the picture, but that is a really tentative and unreliable identification. If Belgian, it probably dates for either before WWI or the 1920s and probably would have been marketed by Anciens Etablissements Pieper, although not necessarily made by them. I forget off hand when AEP ceased marketing of ammunition under their name.
If you have the projectile, check it for jacket material (CN or CNCS likely). If CNCS, then I would say it is likely (not positively) not Belgian, and then possibly Austrian or Italian.
Best I can do with this. Sorry it is an inadequate answer.