What are the legitimate Islamic guidelines that a menstruating woman must follow to memorize and recite the Holy Quran without touching the Mushaf?

It is not permissible for a menstruating woman to touch the Mushaf (definition) (copy of the Qur’an) directly without an interposing barrier, according to the majority of scholars, due to the Almighty’s saying: (None touch it except the purified) [Al-Waqi’ah: 79], and the saying of the Prophet, peace and blessings be upon him: "No one should touch the Qur’an except one who is pure." Similarly, it is not permissible for her to recite the Qur’an, according to the majority of scholars, based on the saying of Ali, may Allah be pleased with him: "The Messenger of Allah, peace and blessings be upon him, was not hindered from reciting the Qur’an by anything except janabah (definition) (major ritual impurity)," and they considered a menstruating woman to be like one in a state of janabah.

However, some scholars hold the view that it is permissible for a menstruating woman to recite the Qur’an, unlike one in a state of janabah, and this is the more preponderant opinion, due to the long duration of menstruation and what prohibiting her from recitation might cause in terms of forgetting the Qur’an. Some of them also held that it is permissible for a menstruating woman to touch the Mushaf with an interposing barrier when there is a need, such as for memorization and revision. Indeed, Ibn Taymiyyah even went so far as to say that it is obligatory for her to do so if she fears forgetting.