Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
- If the adhan for Fajr is given and a person has not yet prayed witr, he should delay it until the forenoon, after the sun has risen high. Then he should pray whatever he can, two or four rakahs or more, two by two.
- If his habit is to pray three and he did not pray them at night, he should pray them in the forenoon with four rakahs and two taslims and so on.
Answering your question about the permissibility of praying witer after adhan of Fajr, the late Saudi scholar, Sheikh Ibn Baz (may Allah have mercy on him) stated:
Time for Witr
The time for praying Witr ends when dawn comes. Prophet Muhammad (peace be upon him) said: ‘The night prayers are two by two, then when you fear that dawn is about to break, then pray one (rakah). And make the prayers that you have offered odd-numbered.” (Al-Bukhari)
Abu Saeed Al-Khudri reported that the Prophet said: “Pray Witr before dawn comes.” (Muslim)
Making Up Missed Witr
If the adhan for Fajr is given and a person has not yet prayed witr, he should delay it until the forenoon, after the sun has risen high. Then he should pray whatever he can, two or four rakahs or more, two by two.
If his habit is to pray three and he did not pray them at night, he should pray them in the forenoon with four rakahs and two taslims.
If his habit is to pray five and he was not able to do them at night because he was sick or he was asleep and so on, he should pray them in the forenoon with six rakahs and three taslims, and so on.
What Was the Prophet’s Habit of witr?
This is because the Prophet used to do that. He used to pray witr with eleven rakahs. But if sickness or sleep kept him from doing that, he would pray them during the day with twelve rakahs.
This is what Aishah said according to the report narrated from her by Al-Bukhari and Muslim. And this is what is prescribed for the ummah, following the example of the Prophet. (Majmu Fatawa Ibn Baz, 11/300)
Almighty Allah knows best.
Source: www.islamqa.info