Mixed bag:

“...That same year [1935] while passing through London, the composer Hanns Eisler and singer Ernst Busch met a German who had been “freed” from Börgermoor, who gave them the lyrics and sang them the melody with a few approximations….”

“According to the authors, he was apparently a Gestapo informant.”
[Inge Lammel and Günther Hofmeyer, eds., Lieder aus den faschistischen Konzentrationslagern (Leipzig: Friedrich Hofmeister, 1962)]
On Discogs:Ernst Busch – 6 Songs For Democracy

Note: Both the American's Keynote and Stinson record labels were de facto Stalinist franchises (Amkino, NKVB, GUGB &c. &c.) The movie (below) would/should have been running in their American cinemas at the time.

Mudcat Zhankoye thread mentioned above: Origins/lyrics: Hey Zhankoye

The Yiddish-Soviet titles are closer to “Swamp” soldiers.

Same late 1930s Lefty-v-Nazi theme, no song (soundies were still new tech.) Peat-Bog Soldiers. Ukrainian actor Ivan Koval-Samborsky (1893 – 1962)(Walter in the film) was himself a Soviet political prisoner before the movie even premiered. It's available on yTube and Archive.org if that's your thing.

But, faded-jaded memory says this one might be closer to the North American's Organization for Jewish Colonization in Russia and Birobidzhan.
(Biro-Bidjan in Yankee-English)