tax problem of J1 to H1,Help!

My hu*****and was a J1. His J1 will expire in Jan. 2004. He changed his status from J1 to H1 in October, 2003. He never filled any form about his tax because he thought J1 should not pay tax. He is preparing for green card application now. Is he in trouble? What should he do? Thank you for your advice!