Red Army-Russia:
The Red Army captured many german tanks in the later years of the war, and the Panther was especially "popular" with the russian forces, who used them alongside their own tanks. The Red Army had several Panthers also after the war ended, but they did not (as far as I have been able to find) se active duty after spring 1945.
Bulgaria:
Bulgaria received 15 captured Panthers from the Red Army spring 1945, these were used for training purposes. Many of them ended up dug down as pillboxes on the Bulgarian-Turkish border already in the late 1940`s. The exact fate of these are unclear, but they were probably scrapped in the 1950`s.
Romania:
Romania received 13 Panthers from the USSR in 1946, who formed the 1.st Armored Brigade but but in 1947 the equipment was ceded to the Soviet-organized "Tudor V. Division" which was transformed from a volunteer infantry division into an armored one. The Panther tank was officially known as T-5 in the Romanian army. These tanks were in bad shape and remained in service only until about 1950, when the Romanian Army received T34-85 tanks from the USSR. All of the Panther tanks were scrapped by 1954.
Sweden:
Sweden picked up a Panther i France in 1946, this was used in Sweden fopr training and testing until 1961.
France:
France had the largest number of Panthers after the war, and they actually equipped the 503e Régiment de Chars de Combat with fifty-yes 50- Panthers after the war! These remained in service until 1950
Not good quality photo but as far as I have found, this is French Panthers with the 503.th around 1947
Great Britain:
After the war a few (some sources indicate 9 total) Panthers were in fact built- under allied control of course. Two (one PAnther and one Jagdpanther) were sent to Britain for testing and trials. They are now both at the Bovington Tank Museum, Dorset.
