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
وَحَدَّثَنَا عَمْرٌو النَّاقِدُ، حَدَّثَنَا سُفْيَانُ بْنُ عُيَيْنَةَ، عَنْ عَبْدِ اللَّهِ بْنِ أَبِي لَبِيدٍ، سَمِعَ أَبَا سَلَمَةَ، قَالَ أَتَيْتُ عَائِشَةَ فَقُلْتُ أَىْ أُمَّهْ أَخْبِرِينِي عَنْ صَلاَةِ رَسُولِ اللَّهِ صلى الله عليه وسلم . فَقَالَتْ كَانَتْ صَلاَتُهُ فِي شَهْرِ رَمَضَانَ وَغَيْرِهِ ثَلاَثَ عَشْرَةَ رَكْعَةً بِاللَّيْلِ مِنْهَا رَكْعَتَا الْفَجْرِ .
Abu Salama is reported to have said. I came to 'A'isha. I said: O mother, inform me about the prayer of the Messenger of Allah (ﷺ). She said: His (night prayer) in Ramadan and (during other months) was thirteen rak'ahs at night including two rak'ahs of fajr.