Night prayers and the number of rak`ah offered by the Prophet (ﷺ) at night, and that Witr is one rak`ah, and a one-rak`ah prayer is correct
حَدَّثَنِي هَنَّادُ بْنُ السَّرِيِّ، حَدَّثَنَا أَبُو الأَحْوَصِ، عَنْ أَشْعَثَ، عَنْ أَبِيهِ، عَنْ مَسْرُوقٍ، قَالَ سَأَلْتُ عَائِشَةَ عَنْ عَمَلِ، رَسُولِ اللَّهِ صلى الله عليه وسلم فَقَالَتْ كَانَ يُحِبُّ الدَّائِمَ . قَالَ قُلْتُ أَىَّ حِينٍ كَانَ يُصَلِّي فَقَالَتْ كَانَ إِذَا سَمِعَ الصَّارِخَ قَامَ فَصَلَّى .
Masruq is reported to have asked 'A'isha about the action (most pleasing to) the Messenger of Allah (ﷺ). She said: He (the Holy Prophet) loved (that action) which one keeps on doing regularly. I said (to 'A'isha): When did he pray (at night)? She replied: When he heard the cock crow, he got up and observed prayer.