Answered by Shaykh Faraz Rabbani
Is it permissible to take the ghusl after sleep, for example before the morning prayer or do you have to take the ghusl before you fall in sleep and what if you fall in sleep without taking ghusl?

Walaikum assalam wa rahmatullah,
Yes, it is permitted. Sayyida A’isha (Allah be pleased with her) reported that the Prophet (Allah bless him and give him peace) did it occasionally. However, he (peace and blessings be upon him) would wash his private parts and performed wudu. [Bukhari and Muslim]
The scholars explain that one should minimally wash one’s private parts, and ideally perform wudu as wellthough this wudu does not enable one to perform any worship impermissible for someone in a state of major ritual impurity. [Ibn Abidin, Radd al-Muhtar]
However, it is best to hasten to perform ghusl, as this was the habit of the Prophet (Allah bless him and give him peace). [ibid.]
Wassalam,