Q: Salam Shaykh. What time constitutes tahajjud? Can we pray only during the last third of the night or other times at night?
A: Wa ‘alaykum al-salam. Night prayer begins after Maghrib and ends at Fajr. It is the best optional Prayer. Making it before the last half of the night is better than the first half though the last 1/3 is best.
Source: Sharh al-Muntaha