Is the Fajr prayer acceptable for one who had intercourse with his wife and then slept until the Fajr Adhan, then delayed performing ghusl due to the absence of a water heater or his sleep, and did not pray until an hour or more after sunrise?

Negligence in performing prayer on time is among the major sins, and it is not permissible to intentionally delay it beyond its time. The time for Fajr prayer ends at sunrise, and a prayer performed after its time has elapsed is considered a make-up (qada'). One must be diligent in performing prayer on time by fulfilling its conditions, such as ghusl (definition) (ritual bath). There is no harm in sleeping before performing ghusl after janabah (definition) (ritual impurity).