What is the ruling on one who had intercourse with his wife at night, then slept until Fajr, then performed ghusl and went to prayer?

There is no harm for a person in a state of major ritual impurity (junub) to sleep before performing ghusl (ritual bath). It is, however, recommended for him to perform wudu (ablution) before sleeping. This wudu is not obligatory according to the majority of scholars. The Prophet, peace and blessings be upon him, used to sleep while in a state of junub after washing his private parts and performing wudu.