If the Muslim prays Witr then he wants to pray qiyaam al-layl after that, he should pray them two by two, and he does not have to repeat Witr.
The Prophet (peace and blessings of Allaah be upon him) commanded that the last prayer offered at night should be Witr, but this command is in the sense that is it mustahabb, not obligatory. See Question no. 37729 .
Shaykh Ibn Baaz was asked:
If I have prayed Witr at the beginning of the night, then I get up to pray qiyaam at the end of the night, how should I pray?
If you have prayed Witr at the beginning of the night then Allaah enables you to get up at the end of the night, then pray whatever you can two by two – without Witr, because the Prophet (peace and blessings of Allaah be upon him) said: “There cannot be no two Witrs in one night.”
And it was narrated from ‘Aa’ishah (may Allaah be pleased with her) that the Prophet (peace and blessings of Allaah be upon him) used to pray two rak’ahs after Witr sitting down. The reason for that – and Allaah knows best – was to show the people that it is permissible to pray after Witr.
Majmoo’ Fataawa al-Shaykh Ibn Baaz, 11/311
And Allaah knows best.