AFAIK, the BMW 132 was a license built Pratt @ Whitney R-1690 Hornet, used in Ju 52, Ar 196 and others.
The Russian M-25 was an exact copy of Wright R-1820, later developed into M-62 and M-63 and widely used in I-15, I-152 and I-16 fighters.
The later M-82 (14 cyl, in La-5/7, Tu-2) and M-71/73 (18 cyl, prototype fighters and Tu-4, which was itself a copy...) were based on these earlier 9-cyl desingns.
Also these russian engines were either based or copied from foreign designs:
-Shvetsov M-87, later developed to M-88, a 14-cyl radial that was a licence built Gnome-Rhone 14N, used in Su-2 light bomber and DB-3/Il-4 medium bomber
-Klimov M-100, later developed to M-103,105 and 107, very widely used in SB-2, Pe-2, LaGG-3, and all Yakovlev fighters, license built Hispano-Suiza 12Ybrs and then developed further. Some SB-2s with the M-100 were shot down over Finland and the Finns thought the engines were Hispanos, so they must have been very similar.
-And last but not least, Soviets built the old BMW VI, a massive old unsupercharged German V-12, most famously powered the He 51, first succesful Nazi-Germany fighter. Mikulin M-17 was the first model, then with superchargers added become M-34,35,38, and 42, very widely used in TB-3, MBR-2, Il-2, MiG-3, and Il-10.
So, most of the engines USSR used during WWII were not exact copies, but still were based on older, foreign designs and improved further, usually much further than the original designs were (AM-series, M-105/107).