Complex sentence: According to Kanin's autobiography, Cukor did not like Mannheimer's work, believing it lost much of the value of the play, so he approached the playwright about writing the screenplay from his own play.
Split into simpler sentences: According to Kanin's autobiography though, Cukor did not like Mannheimer's work, and thought it lost much of the value of the play. Thus he approached the playwright about writing the screenplay from his own play.