All praise is due to Allah, blessings and peace be upon Prophet Mohammad and upon his family and companions.
The Witr prayer is a confirmed sunnah, has the same conditions of voluntary prayer, and is offered in manners that vary according to their reward
The first manner which is the most preferable: is separating each pair of Rakahs with a Tashahud (saying ashhadu ana la illah illalah) and a Tasleem (saying Alsalamu Alikum Warahmatu Allah at the end of the prayer) which is better than praying them continuously based on Aisha`s Hadith which reads as follows: “The Prophet (PBUH) used to pray, after Isha and before Fajir prayers, eleven Rakahs where He offered Tasleem between each pair, and prayed the eleventh Rakah as Witr.” {Bukhari and Muslim}.
The second manner: is offering all Rakahs continuously and ending them with a final Tashahhud.
The third manner is offering Rakahs continuously with two Tashahhuds, this is the lowest in reward: to differentiate it (Witr prayer) from Maghrib prayer since a Hadith reads: “Offer not Witr prayer like Maghrib prayer.” Narrated by Al-Darkotni who said: "a sound chain of narrators."
It is stated: “The minimum of Witr is one Rakah and the maximum (complete) is eleven Rakahs with each pair concluded with one Tasleem. However, the minimum of the complete Witr is:three Rakahs with two Tasleems….and a person is free to perform three and eleven Rakahs with one Tasleem. He is also allowed to offer Tashahhud after the tenth and the eleventh Rakahs. Two Tashahhuds are better as more than that renders the prayer null and void." [Umdat Al-Salik, pp./60]
Accordingly, it is permissible for the questioner to offer Witr prayer in three Rakahs with a single Tashahhud. And Allah Knows Best .