Answered by Sayyidi Habib Umar bin Hafiz (may Allah protect him and benefit us by him)
I have a routine of praying tahajjud, reciting the Qur’an and adhkar before Fajr. If I wake up late and am unable to do all of these things what should I do?
You should do a little bit of everything: pray a few units of tahajjud, recite some Qur’an and recite some of the adhkar. Then you should make up whatever you missed between sunrise and midday. The Prophet ﷺ said that if someone oversleeps and fails to perform the prayers that he regularly performs at night but then makes them up between sunrise and midday it will be recorded for him as if he prayed it at night.