In 1948–1951, Konstantinopolsky won the 1st Soviet Correspondence Chess Championship. He was awarded the title of International Master (IM) in 1950, that of International Master of correspondence chess (IMC) in 1966, and that of Honorary Grandmaster (HGM) in 1983. According to his game files, he only had one chance to play over-the-board in an international tournament outside the Soviet Union, the 'B' section of Amsterdam 1966, when he was well past his prime at age 56. Even so, he scored a creditable 5/9. He continued to work as one of the Soviet Union's most respected trainers well into his 70s.