This story is quite plausible, since we know for sure that money of different marks were actively used by Soviet armed forces throughout the entire war, including (but not limited to) the Allied currency.

Reasons for this are simple and stem from the method in which the Red Army operated. For many combat activities, including confirmed destruction of enemy tanks, soldiers were paid substantial rewards in currencies which were available at hand, and this was deemed as a worthy technique in increasing troops' aggressiveness and initiative during warfare. Besides, since very considerable amount of fighting in the East happened in rural areas it was deemed to be normal for soldiers to engage in small-scale trade with the locals (was very common in Romania and Hungary), often using it to somewhat broaden their combat ratio and/or substitute for materials lost in battle/not yet delivered by rear services. Organizing and delivering suitable money consignment became a major problem during late stages of war because of already huge and ever increasing distances away from Soviet banks and money making apparatus and relatively low Red Army's level of mechanization and constant lack of free transporting vehicles: sometimes money had to be delivered by plane in an urgent situation when frontal troops needed to readjust their budgeting.

In order to lessen the burden upon USSR's banking system and ease money usage on newly captured territories Soviet command decided to implement different currencies, primarily those which were in use on said territories. During Jassy-Kishinev Offensive Operation it was common practice to regiser combat deeds and pay for them in Romanian liras - either paid for (by advantageous rouble course, of course), taken by demand from local administration or captured from the enemy. It is quite possible that besides Romanian liras, Polish zloty, German reichsmarks and several others, Allied supplies were also broadly used since USD was quite valuable even in 1940s.

Sources:

Der Spiegel/Profile, "Monetary systems and cost of war of the Soviet Union in WW2", 2015

Dmitry Loza's memoirs, precisely his experience in acquiring Romanian liras for his service, 2000