Is it permissible to perform the Night Vigil Prayer (Salat al-Layl) after the Witr prayer and before sleeping, due to the inability to perform it in the last part of the night?

The basic principle is that the night prayer (Qiyam al-Layl) should conclude with Witr, based on the Prophet's (peace be upon him) saying: "Make the last of your prayers at night Witr." If one prays Witr and then wishes to pray after it, that is permissible, but one should not repeat Witr, based on the Prophet's (peace be upon him) saying: "There are no two Witrs in one night." It is permissible to intentionally pray Witr early with the intention of praying after it, but this is disliked by the Malikis, unless the intention to perform supererogatory prayers arises unexpectedly after or during Witr, and there is a normal pause between Witr and what follows it.