Did the Germans or other Axis use .380 / 9MM K in world war II?

In 1968 the PPK/S was developed under license by Interarms when the PPK failed to qualify for importation under the Gun Control law. Not until then was it chambered in 380.

During the war the Ortgies, Mauser HSc and Astra 300 were available and chambered in 9mm kurz.

Correction: after investigation I find the PP, PPK and PPK/s were all available in 380 but the gun control act stopped importation. Walther re-designed the piece and Interarms was the distributor.

Yes.

"The .380 ACP has experienced very widespread use in the years since its introduction (1908 USA, 1912 Europe). It was used by Gavrillo Princip to assassinate Archduke Franz Ferdinand and his wife Sophia, the event which is credited with starting the First World War. It was later adopted by the armies of at least five European nations as their standard pistol cartridge before WWII; Czechoslovakia (Vz.38), Hungary (FEMARU 37M), and Italy, all of whom used domestic designs, as well as The Netherlands and Yugoslavia, both of whom adopted the FN Model 1922. It was also used extensively by Germany, who captured or purchased hundreds of thousands of pistols in this caliber during World War II. Popular German built commercial models, such as the Walther PPK were very popular with German officers. The Italian Army used the Beretta M1934, but the Italian Air Force and Navy stuck with the 7.65mm/.32 ACP when they adopted the Beretta M1935."

The 9mm Kruz was their standard police round. After WW I they were forbidden to make military weapons and ammo. The 9mm was military, so they shortened the case by 1 mm, called it the 9mm short and got around the ban.

Gee, I wonder....