If I do not pray Witr until the dawn (Fajr) athan, is my Witr prayer valid, and how should I pray it?

The majority of scholars hold that the final time for the Witr prayer is the break of dawn (true dawn), and if one misses Witr, it should be made up in the daytime as an even number of rak'ahs.

Some scholars are of the view that the time for Witr extends until the Fajr prayer. They cite hadiths and narrations from the Companions as evidence. Some Maliki scholars believe that Witr has an optimal time, which ends at the break of dawn, and a time of necessity, which extends until the Fajr prayer.

Scholars differ concerning making up Witr after the Fajr prayer: some consider it impermissible because it is a time when prayer is prohibited, while others deem it permissible because it is one of the prayers that have a reason [for their performance]. Some scholars opted for making it up after the sun has risen.

In summary: The time for Witr ends at the break of dawn according to the majority of scholars, and it is to be made up as an even number of rak'ahs thereafter.