Is it permissible to make up the Qiyam al-Layl prayer for one who woke up late and prayed the Witr (odd) rakah, and then dawn broke, given that he used to regularly pray eleven rakahs every night?

The minimum for Witr is one rak'ah, and the minimum for its perfection is three rak'ahs. Whoever misses Qiyam (definition) al-Layl due to sleep is legislated to make it up after the permissibility of the supererogatory prayer until the time of Dhuhr prayer. It is recommended to make up for missed temporary supererogatory prayers, and whoever misses his litany (wird) from night or day, let him make it up to maintain his consistency in remembrance. Whoever sleeps through his portion (hizb) of the night or a part of it and recites it between Fajr and Dhuhr, it is written for him as if he recited it at night. And if the Prophet, peace and blessings be upon him, missed his portion of the night, he would make it up during the day with twelve rak'ahs, and Witr is made up along with its Shaf' (even number of rak'ahs before Witr).