I too am a firm believer that Jeffery did not design the 500 as their own literature doesn't make any mention of doing so.
Reading their period advertisements, you will notice that they do make a point of claiming the design of the 404 but their use of the 500 in the Mauser magazine rifle is at the behest of their customers.
I think that this indicates pressure from the field to chamber their rifles in an already existing cartridge.
It would be unthinkable for an English maker NOT to indulge in the accolades of creating the most powerful bolt action cartridge ever devised!

See here:
https://www.theexplora.com/the-classic-w-j-jeffery-co-safari-rifles/

Also, there has been much debate over whether the 500 was ever loaded with strand cordite. As far as I am aware, no example has ever been produced. There is still a standing reward on AR for anybody able to prove that the 500 was a cordite cartridge in period by pulling a bullet of an original cartridge. The fact that flake powder load was exclusively used is more support that the 500 was a German development.