If someone decides to offer Witr prayers at Tahajjud time but does not get up and misses Witr prayers, then it should be remembered that from the Azan (call to prayer) of Fajr, up until sunrise there are no prayers apart from the two Sunnah of Fajr and the two compulsory rak’aat of Fajr.
The jurists generally say that if someone missed their Witr prayers, they have the option of offering them after sunrise.
However, it should be remembered that the Holy Prophet(sa) paid great importance on the Witr prayers and its offering at the correct time. His Sunnah (practice) should be followed and if someone is doubtful as to if they will get up and offer them in time after sleeping, then it is strongly advisable to offer them before sleeping after Isha prayers.
The Promised Messiah(as), Hazrat Mirza Ghulam Ahmad would offer his Witr prayers after Isha before going to sleep, and later, after awakening, would then offer Tahajjud prayers in the morning.