Fiqh-us-Sunnah Volume 2, Supererogatory Prayer, Fiqh 2.024A.

Salatul Layil may be performed in the early part of the night, the middle part of the night, or the latter part of the night, but after the obligatory salatul ‘isha.

While describing the salah of the Prophet sallallahu alehi wasallam, Anas would say: “If we wanted to see him praying during the night, we could see him praying. If we wanted to see him sleeping during the night, we could see him sleeping. And sometimes he would fast for so many days that we thought he would not leave fasting throughout that month. And sometimes he would not fast (for so many days) that we thought he would not fast during that month.” This is related by Ahmad, al-Bukhari, and anNasa’.

Commenting on this subject, Ibn Hajar says: “There was no specific time in which the Prophet sallallahu alehi wasallam would perform his late night prayer; but he would do whatever was easiest for him.”