Answer
(Fatwa: 1546/1550/M=1430)
The salah offered in the night after awakening is called Tahajjud. It is better to perform it in last night, however it may also be offered in midnight. And the person who is unable to wake up in last night or midnight, he may offer two or four raka?at with the intention of tahajjud after Isha prayer. Insha-Allah he shall get its reward. The night shall be divided into three parts from sunset to dawn (before the starting of fajar time) not the time of sunrise.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband