What is the ruling on my fasting after I had intercourse with my wife at night and then fell asleep and did not perform ghusl until after Fajr, then ate, thinking that my fast had been invalidated?

The fast of one who wakes up in a state of major ritual impurity (junub) in Ramadan is valid, based on what was authentically reported from Aishah and Umm Salamah, may Allah be pleased with them both, that the Prophet, peace and blessings be upon him, would wake up in a state of major ritual impurity due to intercourse, then he would perform ghusl (ritual bath) and fast. The husband must fear Allah and refrain from issuing religious rulings without knowledge. He bears the sin for his wife breaking her fast without a valid excuse, and she must make up that day.