Jack Teagarden left Whiteman when his contract expired at the end of 1938 to form his own band. However, his brother Charlie did not immediately join him, but stayed with Whiteman until the latter broke up his band at the end of May, 1940. Rayno writes (p. 548 of his second volume of *Paul Whiteman: Pioneer in American Music*): "22 May 1940 (Wed) As they did in September 1939, Whiteman and his band visit Bix Beiderbecke's grave in Oakdale Cemetary in Davenport and lay a wreath on it." Actually, technically speaking, Charlie stayed on a little while after the band broke up; he joined Whiteman and three other Whiteman musicians (Harry "Goldie" Goldfield, Al Galidoro, Mike Pingitore) in Los Angeles in June 1940 for the filming of *Strike Up the Band.*
Charlie's presence is clearly audible in a number of 1939-40 Whiteman recordings:
(1) He has a 16 bar solo on the Bouncing Brass's April 6, 1939 recording of Irving Berlin's "Heat Wave": http://picosong.com/wsJ3j/
(2) From the same session, Charlie solos (as does Miff Mole) on another Irving Berlin tune, "Home Again Blues": http://picosong.com/wsJnw/
Jack Teagarden's departure certainly hurt Whiteman's more jazz-oriented performances in 1939-40, but not only did Charlie remain on trumpet, but Whiteman did have two fine jazz trombonists to replace Jack: Miff Mole (whom Whiteman had wanted in the band back in the 1920's...) and Moe Zudekoff (later to be known as the bandleader Buddy Morrow). So the band--or units from it--could play creditable jazz on occasion.