During World War I, he moved to Moscow. In 1916, he tied for 4-5th, and was 3rd in 1918. He tied 5-7 at the Russian Chess Olympiad (1st United Research Services-ch) at Moscow 1920.
In 1922/23 he took 10th in the Moscow City Chess Championship.
In 1924 he took 10th in the 5th Moscow City Chess Championship. In 1943 Rabinovich starved to his death.
Abram Rabinovich vs Alexander Alekhine, Carlsbad 1911, Caro-Kann Defense, Advance Variation, B12, 1-0
Alexander Ilyin-Zhenevsky vs Abram Rabinovich, Moscow 1920, 1st United Research Services-ch, Ruy Lopez, Morphy Defense, Anderssen Variation, C77, 0-1
Abram Rabinovich vs Sergey von Freymann, Moscow 1924, 3rd United Research Services-ch, Zukertort Opening, Dutch Variation, A04, 1-0.