Complex sentence: Oleg Lundstrem's Big Band, and "Allegro", and soon after that got wide recognition in the USSR, becoming known as the best tenor saxophonist, placing first in the Soviet Critics' Polls and recording some albums for "Melodiya" label.
Split into simpler sentences: Oleg Lundstrem's Big Band, and "Allegro", and soon after that got wide recognition in the USSR. Igor became known as the best tenor saxophonist, placing first in the Soviet Critics' Polls and recording some albums for "Melodiya" label.