From the information I have, the only tank that was used by the Italians on the Eastern front was the L6/40 as well as the Semovente L40 da 47/32 based on the same chasis. The M13/40 series (including the M14/41 and M15/42) were not employed by the Italians there. Some M13/40's were used in Greece and Yugoslavia in 1941/42 with the Centauro and Littorio Divisions. Armor units used in the Eastern Front were independent battalions.
After the armistice of 1943, the Germans used a large variety of Italian armor for anti-partisan work. You would see L3/35 used in this role throughout the Balkans as well as the AB41 series of armoured cars. In the Panzer Wrecks series of publications there is alot of pictures of these vehicles including the M13/40 series used in anti-partisan units. The vehicle in Warsaw, I believe was from one of those units. This is what information that I have on that one in Warsaw. It wasn't used by the Home Army, guessing that it broke down.
German Panzerkampfwagen M14/41 736(i) (Italian Carro Armato M13/41) medium tank
Single tank captured.
Two T-34's were captured by the Italians and used on the Eastern Front and at least one T-28
During WWII, the Italians had only 3 armoured divisions which played a part in any actions, three additional units never truelly materialized. Italian manufacturing had very limited capacity and for most of the time only Ariete was in the field and properly supplied the other divisions were stripped of equipment to maintain Ariete. Like most Italian divisons these units were undersized and more comparable to a British brigade in strength and equipment. None were used in the Eastern Front, the 132nd Ariete was the first completely equipped and used only in North Africa until it was dissolved after the second battle of El Alamein.
The 131st Centauro Divison was actually used first in Greece and Yugoslavia with Littorio but was recalled to Italy for replenishment. Use against prepared Greek position in the mountains was at a disavantage to the armor and they suffered greatly. It was last used in North Africa/Tunisia, played a part at Kasserine and eveuntually surrendered to Allied forces.
133rd Littorio was the other formation, used in Yugosalvia, but destroyed at second El Alamein alongside of Ariete.
Mike T.
Beware the hobby that eats. - Ben Franklin
Do not fear mistakes. You will know failure. Continue to reach out. - Ben Franklin
The U.S. Constitution doesn't guarantee happiness, only the pursuit of it. You have to catch up with it yourself. - Ben Franklin