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Is it permissible for me to go to sleep when I am Junub (due to intercourse) and wake up at the time of Fajr prayer to do Ghusl?
Praise be to Allah.
It is permissible for one who is Junub to go to sleep before doing Ghusl , then wake up to do Ghusl before praying Fajr.
The evidence for that is the report narrated by At-Tirmidhi (110) from `Aishah (may Allah be pleased with her), who said: The Messenger of Allah (blessings and peace of Allah be upon him) would go to sleep when he was Junub without touching water. (Classed as authentic by Al-Albani in Sahih At-Tirmidhi, 103)
But it is better for him to do Wudu before going to sleep, and if he does Ghusl that is best.
It was narrated from `Aishah (may Allah be pleased with her) that she was asked: What did the Messenger of Allah (blessings and peace of Allah be upon him) do when he was Junub? Did he do Ghusl before going to sleep, or did he go to sleep before doing Ghusl? She said: He did both; sometimes he would do Ghusl then go to sleep, and sometimes he would do Wudu then go to sleep. (Narrated by Muslim, 465)
`Umar (may Allah be pleased with him) asked the Prophet (blessings and peace of Allah be upon him): Can one of us go to sleep when he is Junub? He said: Yes, if he has done Wudu. (Narrated by Al-Bukhari, 280 and Muslim, 462)
For more details, please refer to the following answers: 20847 , 14225 , 7310 , and 10319 .
And Allah knows best.