Ok, so we're looking at something like the Soviets who observed the course of the war noting the way the 88mm gun was used more as an AT and artillery piece than in the AA role. They might be attracted to the idea as a means of simplifying supply and logistics - if the same gun design can do 3 jobs (heavy AA and AT as well as light artillery), that helps matters both in terms of maintenance and manufacture. So the idea comes back to Moscow and someone thinks enough of it to institute a study for a suitable weapon.
Then WW2 kicks off in 1939, and gives the project a bit more urgency.
In the end, three candidates for this are identified - the
76mm AA gun which is currently in service, the
85mm AA gun which is just about to enter service, and the German 88mm itself - a few examples were captured during the Spanish Civil War, and perhaps Communist sympathisers have got enough details out for the USSR to have a stab at constructing one themselves.
At first, it looks like the 76mm gun will win - it's a standard calibre already in the Red Army, which reduces the disruption of switching to it in three roles and means that the tooling and support network already exists, and it's thought to be capable of defeating the armour on any current tank. But in the Battle of France, the Char B1 and Matilda tanks prove to stand up well against the German AT weapons. It's obvious the Germans will have learnt from this experience, and AT weapons will have to get heavier as armour increases. For several months after the fall of France, discussion rages among the committee members overseeing this project: is it better to go ahead with the 76mm gun because it can be supplied sooner and in greater quantities, despite the fact it may not be adequate against the next generation of tanks; or should the 85mm be chosen for it's greater potential? A small but vocal minority holds out for as close to a direct copy of the German 88mm as Soviet industry can manage, but the 85mm is eventually chosen. There are two main reasons for this: firstly, production of the 76mm has already ceased and output of the 85mm is picking up as it takes over the medium/heavy AA role. Secondly, there just isn't time to reverse-engineer the 88mm and put it into production, especially since it would be duplicating the role of the 85mm. This leaves the 85mm selected by default, and the committee recommends that the numbers procured be significantly increased with the aim of standardising on this gun for all medium/heavy AT and AA, along with light artillery batteries.
By the end of 1940 the increased allocations are starting to reach their units - AA formations receive theirs first, but a few have reached AT gunners as well. As 1941 rolls on the numbers increase - a few artillery units are now equipped with the new weapon. But the re-equipment has not been completed before June 1941...