Conkright remained with the Rams through the 1945 season, when the team won the NFL championship. Rams owner Dan Reeves moved the team to Los Angeles after the season, but Conkright decided to stay in Cleveland, where he and his family lived. He took a job as a scout and coach for the Cleveland Browns, a team that was to start play in 1946 in the new All-America Football Conference (AAFC).