Complex sentence: Henry Busse and his Orchestra continued to record and perform up until his death in 1955 at an undertaker's convention at the Peabody Hotel in Memphis while he was playing with his Shuffle Rhythm Band.
Split into simpler sentences: Henry Busse and his Orchestra continued to record and perform up until his death in 1955. Busse died at an undertaker's convention at the Peabody Hotel in Memphis while he was playing with the Shuffle Rhythm Band.