Is it permissible for a sick father to delay Fajr prayer until 6:00 AM if he is unable to complete his sleep after waking up for Fajr prayer at its prescribed time?

We advise the father to change his sleep schedule so that he sleeps after the 'Isha prayer and wakes up at dawn to perform the prayer on time. If he sleeps before the time for the Fajr prayer begins, he must take measures to wake up for the prayer. If sleep overcomes him and he does not wake up until after the time has passed, there is no sin upon him, and he must pray when he wakes up.