How is the fast valid for someone who wakes up in a state of janabah due to intercourse, and was he praying Fajr in this state?

The hadith (definition) does not indicate that the Prophet (peace be upon him) abandoned the Fajr prayer. Rather, all it indicates is that he (peace be upon him) did not perform ghusl (definition) (ritual bath) from major ritual impurity until after the dawn broke, and this is permissible. Al-Qurtubi mentioned two benefits from this: the permissibility of delaying ghusl until after the dawn breaks, and that this was due to intercourse, not a wet dream, given his (peace be upon him) infallibility.