What is the specific point at which the invocations "Subhan Rabb al-Alamin (Glory be to the Lord of the Worlds)" and "Subhan Allah wa bihamdih (Glory be to Allah and praise be to Him)" are to be recited, which the Prophet used to say upon rising at night, and is it recited within the prayer, outside of it, or at a particular point during it?

Al-Nasa'i, Al-Tirmidhi, and others narrated the hadith (definition) "Subhan al-Malik al-Quddus" (Glory be to the King, the Most Holy). The word "al-hawiy" in it means a period of the night or a long period of time. Scholars have differed regarding the place for reciting this dhikr: some are of the view that it is among the opening supplications in the night prayer, while others believe it is to be recited upon waking up from sleep. The matter in this regard is broad, and whoever recites it in either of these two instances has done well.