During the height of the Allied supply problems of fall 1944, the United States turned to using captured German (including weapons the Germans themselves had captured from the Soviets and French) artillery pieces and ammunition to stave off a temporary, but crippling, ammunition shortage. The 79th Field Artillery Battalion (Provisional) was formed from personnel of the 79th and 179th Field Artillery Groups and equipped with captured German artillery pieces.
General Patton's Third Army, faced in the fall and early winter of 1944 with a stringent ammunition shortage, refurbished and put into action serviceable items of captured artillery. On 2 November 1944, one corps—the XX—was employing 39 such pieces, classed as follows: four 76.2-mm Soviet guns, ten 88-mm German guns, eight 100-mm fortress guns, six 105-mm German howitzers, two 122-mm Soviet guns, six 150-mm German howitzers, and three 155-mm French howitzers. Up to that date, this corps had fired 30,920 rounds of ammunition weighing 660 tons and valued at $702,391 USD. For the week ending on 29 October of that year, 80 percent of the artillery ammunition fired by the XX Corps had been captured from the Germans. One time-on-target mission fired on a German troop concentration at Amanvillers was executed by U.S. tank destroyers, 90-mm antiaircraft guns, 155-mm M1 howitzers, and by German 105-mm gun howitzers, German 88's, Soviet and French Schneider 155-mm howitzers. The Soviet weapons, and those of the French, had been seized from Allied forces earlier in the war, and had been recaptured by the Third Army.
The 244th Field Artillery Battalion of the U.S. Third Army, normally a towed 155 mm gun battalion, was temporarily re-equipped with captured German artillery pieces. In November 1944, the U.S. First Army formed the provisional 32nd Artillery Brigade, equipped with 48 captured German 105 mm howitzers and 20,000 rounds of ammunition. After the ammunition shortage subsided, the 32nd Artillery Brigade turned to controlling all the 8-inch guns and 240 mm howitzers of First Army.
The 83rd Infantry Division was popularly nicknamed the "Ragtag Circus" by the press due to their willingness to use almost any German equipment they could get their hands on, including halftracks, armored cars, tanks, assault guns, and even a Bf-109.
Sources:
U.S. Army in World War II, by Richard C. Anderson
United States Army in World War II European Theater of Operations: Logistical Support of the Armies September 1944 to May 1945 chapter XX, Supplying the Armies: Ammunition, by Roland G. Ruppenthal
Naturally. A tank, even if it's an enemy tank, is better than no tank.
Due to the evacuation of Soviet factories in 1941, the Red Army was hard pressed for tanks. As a result, the use of captured tanks was quite common. For example, the 107th Independent Tank Battalion was armed with PzIVs, PzIIIs, and StuGs in addition to T-34s and KVs as late as August of 1942.
Of course, an enemy tank is going to work well as long as you keep it supplied. While Soviet gasoline worked with German tanks, Soviet ammunition did not. Proposals to solve this issue were made in February of 1942. The PzIV would be re-armed with the T-34's 76 mm gun, the PzIII and Pz38(t) would take the 45 mm gun from the T-70, the StuG would be re-equipped with the 122 mm howitzer that later went on the SU-122. In practice, only the StuG was used, but for two projects: the SG-122 and SU-76i.
The SG-122 (Samokhdnaya Gaubitsa 122 mm, 122 mm self propelled howitzer) design was finished in early April of 1942. The casemate was made taller and the front armour was increased to 70 mm. Work on a prototype began in June. Trials began in July and ran until mid-August. The mass of the new vehicle was 23.3 tons, compared to the analogous StuH 42.
However, despite successful trials, production was limited by the number of PzIIIs and StuGs that could be captured without critical damage. That number was low: 47 tanks by December 5th, 1942. Meanwhile, the SU-122 was entering production, which provided the same firepower, but without the production constraints. 21 SG-122s were built before cancellation.
The SU-76i (Samokhodnaya Ustanovka 76 mm inostrannaya, foreign 76 mm SPG) was a similar idea, but using the same 76 mm gun as the T-34. A prototype was built in March of 1943, and production continued until December. 201 SU-76i were built. Like the SG-122, this vehicle was also replaced by a domestic design, the SU-76M.
After the war ended, the USSR was going to put all the tanks they captured to good use by digging them in as fortifications, similar to what the Germans did. These tanks would also be re-equipped: the PzIV with an F-34 or ZIS-5, the Panther with the S-53, and the Tiger with the D-10. As far as I am aware, these conversions were never performed.
P. Samsonov Fate of Baryshev's Tank
P. Samsonov Re-arming German tanks
Y. Pasholok Sturmovoye orudiya na trofeynoy baze
A. Statsenko Sovetskiy artshturm