To my knowledge, Enderton was the first to formulate this theorem explicitly. One of the first readers of Enderton’s book in Poland was Roman Suszko, and he was using the theorem. I don't remember Suszko saying that someone else was the author of the Homomorphism Theorem as it is formulated in four parts (a) – (d) on p.96.

Nota bene, I applied Enderton’s Homomorphism Theorem as a lemma in the proof of certain interesting preservation theorem (see my An Essay in Matrix Semantics for Consequence Relations, pages 52–57).

It is worth adding that Andrzej Mostowski in his book Logika matematyczna (Warszawa,1948) formulated and proved in detail a related theorem, an Isomorphism Theorem for higher order logic. See pages 199-203, and especially footnote 1 on page 200. Mostowski’s book is available here

http://matwbn-old.icm.edu.pl/kstresc.php?tom=18&wyd=10&jez=pl

If I remember correctly, Tarski has emphasised somewhere the importance of Mostowski’ proof of the isomorphism theorem.

Also A. Grzegorczyk in his Zarys logiki matematycznej (1961, 1969², 1974³) formulated and briefly commented upon "Theorems on isomorphism” See the enclosed English translation of Zarys …, An Outline of Mathematical Logic, pages 284–285, and p.311.

--Jan (sept 6, 2020)