In serious conflicts, there is always some use of captured enemy weapons on both sides. Sometimes the other guy’s stuff is better, and sometimes there is such a dire need for equipment that anything available is used. Some countries, like Finland, have at times made a whole military industry out of refurbishing and reissuing captured weapons.
Well, Russia was in a pretty desperate situation during World War 2, and needed all the arms they could get their hands on. The newly arrived masses of German soldiers offered one source, and the German weapons were generally pretty good to boot. So of course lots of captured German machine guns were used by Red Army soldiers. Enough that Russian language manuals were printed to instruct soldiers on the proper use and maintenance of the MG34 and MG42. There may have been others as well, but thanks to Hrachya in Armenia, we have copies of these two manuals for your perusal:
(1941) Russian MG34 manual (Russian)
(1944) Russian MG42 manual (Russian)