Ben,
The photos didn't open up. You said the rifle is a 6.3mm. I'm guessing, then, you read that in the proof marks. Is there a case length near the 6.3?, I would likely be somethin in the 50-60mm length, but could be longer or shorter. The 6.3 is the bore(not groove or bullet) diameter, so it would be one of the nominal 6.5mm cartridges. It should be noted that some German 6.5mm cartridges don't use the current standard 6.5mm bullet, which is .264"(6.7mm).If you can get photos to open up( incl. of proof marks)we can give you additional information. Failing that, finding case length will help.
Mike