Solothurn was subsidiary company of Rheinmetall.Solothurn were used by Rheinmetall to design new items becouse Paris/Versailles peace treaty prohibited that directly from german companies.It was SOLOTHURN who designed 20x105B and its bigger "sister" 20x138B with help from Rheinmetall.
I believe they are called "short solothurn" and "long solothurn" around the world,am i right?
Sorry, no! What they are called around the world does not make it correct in any way.
Solothurn was founded in the second half of 1929. As we all know the first model of the 20x138B weapon was the MG C/30 and Flak 30. The development of the Rheinmetall weapons goes back to at least 1928 (and maybe even earlier).
Solothurn only developed the AT rifles, nothing else.
Also we shall not forget that Solothurn was marketing Rheinmetall made weapons (for the reason you gave above). Namely the well known and undisputed 37mm Pak and the 81mm mortar made by Rheinmetall are advertised as Solothurn weapons. Nobody so far ever claimed these to be Soloturn developments or products.
The Solothurn designation originates merely from post war publications written by people who lacked this information.
There are many examples for such errors in ammunition history where information was hard to find or people just liked to use the name of a well known weapon instead a correct designation.
For this reason I never get tired to tell correct designations since in particular we as people with at least some little knowledge have to stick with correct designations. Bending backwards and using incorrect names to please ignorant people who want to keep their old and wrong knowledge can't be our aim.
Last but not least, the Italian M35 Breda is also a Rheinmetall development which got licenced to Italy.
A good friend of mine is currently writing a book on these weapons and the cartridge. I hope it will be out in the next few years. Plenty of facts and info then to be recognized.