Is it permissible for a person who suffers from excess electrical activity in the brain and needs eight consecutive hours of sleep to miss Fajr prayer and make it up later if its time does not accommodate the required sleep duration and they are unable to go back to sleep after waking up?

It is not permissible to delay the prayer beyond its appointed time except for combining the two noon prayers (Dhuhr and Asr) and the two evening prayers (Maghrib and Isha) due to an excuse such as travel or illness. As for Fajr, it must not be delayed beyond its time. Intentionally sleeping until the prayer time expires is like intentionally delaying it, and it is a grave transgression, and some scholars may even consider it major disbelief. If one is overcome by sleep, they should pray upon waking, while taking measures to help themselves wake up. If a trustworthy Muslim doctor determines that sleep is necessary for treatment, then it is permissible to combine Isha with Maghrib in advance (جمع تقديم) and sleep after Fajr or until close to sunrise. In this case, it is permissible to miss congregational prayer. One can arrange to sleep during the day after Fajr, so that Dhuhr prayer is performed before the Asr adhan. There is no harm in combining prayers based on the doctor's statement, but it is not permissible to delay Fajr beyond sunrise.