Can I Pray Witr after Fajr?
Question

What happens if one intends on praying Witr but unintentionally sleeps in or is eating Suhur and loses track of time....can they still pray Witr once the Athan for Fajr has been made?.
Praise be to Allah.When does the time for Witr end?
The time for praying Witr ends when dawn comes , because the Prophet (peace and blessings of Allah be upon him) said: `The night prayers are two by two, then when you fear that dawn is about to break, then pray one (Rak`ah) and make the prayers that you have offered odd-numbered.” (Narrated by Al-Bukhaari, 472) 
Muslim (754) narrated from Abu Sa`id (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: “Pray Witr before dawn comes.”
Can you pray Witr after fajr?
“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 Rak`ahs 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 Rak`ahs 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 Rak`ahs and three Taslims, and so on, because the Prophet (peace and blessings of Allah be upon him) used to do that. He used to pray Witr with eleven Rak`ahs, but if sickness or sleep kept him from doing that, he would pray them during the day with twelve Rak`ahs. This is what `Aishah (may Allah be pleased with her) 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 (peace and blessings of Allah be upon him).” (Majmu` Fatawa Ibn Baz, 11/300) 
Shaykh Ibn Baz (may Allah have mercy on him) was also asked: Should the last of Witr prayer be done when the Adhan begins for Fajr or at the end of the Adhan? If a person sleeps and misses it, should he make it up and how? 
He replied: 
“It is prescribed for every believer, male and female, to pray Witr every night . The time for it is between `Isha’ prayer until dawn begins. It is narrated by Al-Bukhari and Muslim from Ibn `Umar (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: “The night prayers are two by two, then if one of you fears that dawn is about to break, let him pray one Rak`ah to make what he has prayed odd-numbered.” Muslim narrated that Abu Sa’id Al-Khudri (may Allah be pleased with him) said: “Pray Witr before dawn comes.” 
Imam Ahmad, Abu Dawud and At-Tirmidhi narrated, in a report that was classed as authentic by Al-Hakim, from Kharijah ibn Hudhafah (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: “Allah has blessed you with a prayer that is better for you than red camels.” We said: O Messenger of Allah, what is it? He said: “Witr, between `Isha’ prayer and the break of dawn.” And there are many Hadiths on this topic, which indicates that Witr ends with the break of dawn. 
If a worshipper does not know when dawn is, he may rely on a Mu’dhdhin who is known to pay attention to the right time [when giving the Adhan]. If the Mu’dhdhin who pays attention to the right time gives the Adhan, then he has missed Witr. 
As for the one who gives the Adhan before dawn breaks, he has not missed Witr when he gives the Adhan and this does not mean that it has become prohibited for one who is fasting to eat and drink, and the time for Fajr prayer has not begun with this Adhan. 
The Prophet (peace and blessings of Allah be upon him) said: “Bilal gives the Adhan at night, so eat and drink until Ibn Umm Maktum gives the Adhan.” (Narrated by Al-Bukhari and Muslim). Ibn Umm Maktum (may Allah be pleased with him) was a blind man who did not give the Adhan until he was told that dawn had come. From what we have mentioned it is clear that the time for Witr ends with the first Adhan if the Mu’dhdhin pays attention to the correct time of dawn, but if the Mu’dhdhin gives the Adhan when the Muslim is in the final Rak'ah of Witr, he should complete it because he cannot be certain that dawn has come just from hearing the Adhan, and there is nothing wrong with that in sha Allah. 
If a person misses Witr, it is prescribed for him to pray what he usually prays during the day, but he should make it even-numbered by adding one Rak`ah. If he usually prays three, he should make it four, and if he usually prays five, he should make it six, and so on, saying the Taslim after each two Rak`ahs. 
It is narrated by Muslim that `Aishah (may Allah be pleased with her) said: If the Prophet (peace and blessings of Allah be upon him) missed Witr at night because he was sick or sleeping, he would pray twelve Rak`ahs during the day. And he usually prayed eleven Rak`ahs, but if sickness or sleep kept him from doing that, he would pray twelve Rak`ahs as `Aa’ishah (may Allah be pleased with her) said, saying the Taslim after each two Rak`ahs, as `Aa’ishah (may Allah be pleased with her) said: “The Messenger of Allah (peace and blessings of Allah be upon him) used to pray ten Rak`ahs at night, saying the Taslim after each two Rak`ahs, and praying Witr with one.” (Narrated by Al-Bukhari and Muslim). 
And the Prophet (peace and blessings of Allah be upon him) said: “The prayers of the night and day are two by two.” Narrated by Imam Ahmad and the authors of As-Sunan with an authentic Isnad (chain of narration) from the Hadith of Ibn `Umar (may Allah be pleased with him). It is narrated in the books of Al-Bukhari and Muslim with the wording, “The night prayers are two by two,” as we stated at the beginning. And Allah is the Source of strength.” (Majmu` Fatawa Ibn Baz, 11/305-308) 
Shaykh Ibn `Uthaymin (may Allah have mercy on him) was asked: I am keen to offer Witr prayer at the best time for it, before dawn breaks, but sometimes I cannot do it before dawn. Is it permissible for me to pray Witr after dawn breaks? 
He replied: 
“If dawn breaks and you have not prayed Witr, then do not pray Witr, rather pray four Rak`ahs during the day if you usually pray Witr with three, and six if you usually pray Witr with five, and so on. 
Because if the Prophet (peace and blessings of Allah be upon him) missed the night prayers, he would pray twelve Rak`ahs during the day.” (Majmu` Fatawa Ibn `Uthaymin, 14/114) 
It was narrated from a number of the Companions that there is nothing wrong with praying Witr after the Adhan of Fajr until the Iqamah is given – such as Ibn Mas`ud (as was narrated by An-Nasa’i, 1667; classed as authentic by Al-Albani in Sahih An-Nasa’i), Ibn `Abbas (as narrated by Malik in Al-Muwatta’, 255) and `Ubadah ibn As-Samit (as narrated by Malik in Al-Muwatta’, 257) 
Shaykh Al-Islam Ibn Taymiyah (may Allah have mercy on him) was asked about a person who sleeps and misses Witr prayer. 
He replied: 
“He may pray between dawn and Fajr prayer, as `Abdullah ibn `Umar, `Aaishah and others did. Abu Dawud narrated in his Sunan that Abu Sa’id (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings of Allah be upon him) said: “Whoever sleeps and misses Witr or forgets it, let him pray it when morning comes or he remembers.” There are different reports from Ahmad as to whether he should make up the even-numbered Rak`ahs too. The correct view is that he should make up even-numbered Rak`ahs too. 
It is narrated in an authentic report that the Prophet (peace and blessings of Allah be upon him) said: “Whoever sleeps and misses a prayer or forgets it, let him offer it when he remembers it, for that is the time for it.” This includes obligatory prayers, Qiyam Al-layl , Witr and regular Sunnah prayers .” (Al-Fatawa Al-Kubra, 2/240) 
If the Muslim does either of these two things, there is no sin on him in sha Allah. 
And Allah knows best.