Is it permissible to stand during the last third of the night for supplication (Du'a) and glorification (Tasbeeh) during menstruation and at other times, or is it exclusively reserved for prayer?

It is permissible for a woman to spend the last third of the night in supplication, seeking forgiveness, and remembrance of Allah. She may recite the Quran by heart even if she is menstruating, because a menstruating woman is only prohibited from prayer, touching the Mus'haf (physical copy of the Quran), circumambulating the Kaaba (Tawaf), and entering the mosque. The permissibility of remembrance (dhikr) and supplication (du'a) for a menstruating woman is indicated by what the Prophet, peace and blessings be upon him, said to Aisha when she menstruated while in the state of ihram for Hajj: "Do everything a pilgrim does, except circumambulate the House until you become pure."