All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
A person is declared to be a Muslim if he utters The Two Testimonies of faith and abides by the apparent Islamic rites, like the prayer, etc.
Since that man does not pray, it is not permissible for you to accept to marry him, especially that there are some people who pretend to be Muslims for personal reasons then later the reality is otherwise, so you have to be cautious.
That man should be advised to contact the Ministry of Endowment or one of the Islamic Foundations which are on the methodology of Ahlus-Sunnah Wal-Jamaa'h, so that they would teach him the correct Islam.
Allaah Knows best.