"Hey you friend, why are you a fool? I will tell you, I will sing to you: One is God, What is in the heavens, what is on the earth, one (who is) our god. our work, our friendship (is) our Judasim.
Two are our Luchos...."
I recall hearing from Reb Avrohom Lison whose father learned in Lubavitch, that this Niggun (also known as Echad Mi Yodeah in Russian) was already sung in Lubavitch. Rabbi Berel Zaltzman heard it from his father. It was first sung by the Rebbe in the month of Tishrei 5732 as mentioned earlier. The Rebbe showed a special liking to this song and this was the song that Rabbi Berel Zaltzman would usually sing by the Rebbe when he was present by the Rebbe, see for example the beginning of the Farbrengen of Purim 5733 (It’s interesting to note, that before 5732, Rabbi Hirshel Chitrik tried to sing this Niggun by the Rebbe but the Rebbe didn’t encourage it).
In the 5730’s, the Rebbe would ask that this Niggun be sung often and in the 5740’s it was sung at many a Kos Shel Bracha by another Russian Chazzan, Reb Binyomin Tzatzkes. The Rebbe even spoke Sichos in which he explained the meaning of this Niggun (see 10 Shevat 5733). In the later years, Chazzan Binyamin Tzatzkes added the number 14 to the song: "Tsertinatzet Knizriek Rambamah" (14 are the books of the Rambam) to the Rebbe’s great satisfaction.
Chazzen Tzatzkes singing it by the Rebbe
Berel Zaltzman