He chose to say the qunūt before the bowing, and this is the view of some scholars, and it is the view held by Sufyān al-Thawrī, Ibn al-Mubārak, and Isḥāq(1).

It has been related from ʿAlī ibn Abī Ṭālib that he would not say the qunūt except in the latter half of Ramadan, and he would say it after the bowing. Some scholars adopted this view, and it is the view held by al-Shāfiʿī and Aḥmad.

‌‌11 - Chapter on what has been reported concerning a man who sleeps through the witr or forgets it

469 - Maḥmūd ibn Ghaylān narrated to us, he said: Wakīʿ narrated to us, he said: ʿAbd al-Raḥmān ibn Zayd ibn Aslam narrated to us, from his father, from ʿAṭāʾ ibn Yasār, from Abū Saʿīd al-Khudrī, who said: The Messenger of Allah, peace and blessings be upon him, said: "Whoever sleeps through the witr or forgets it, let him pray it when he remembers and when he wakes up"(2).

470 - Qutaybah narrated to us, he said: ʿAbd Allāh ibn Zayd ibn Aslam narrated to us, from his father, that the Prophet, peace and blessings be upon him, said: "Whoever sleeps through his witr, let him pray it when he wakes up in the morning."

This is more sound than the first hadith.

I heard Abū Dāwūd al-Sijzī—meaning Sulaymān ibn al-Ashʿath—say:--------------------------------------------
(1) In the edition of Shaykh Aḥmad Shākir and in Tuḥfat al-Aḥwadhī there is an addition: "and the people of Kufa," which is not found in our manuscript sources nor in the copy upon which al-ʿIrāqī wrote his commentary.
(2) A sound hadith, narrated by Abū Dāwūd (1431) and Ibn Mājah (1188). It is in al-Musnad (11264), and al-Ḥākim declared it sound, 1/302.