Answer
Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
There is nothing wrong with menstruating woman or a woman in post-natal bleeding to recite the Quran. She should not touch the mushaf (a copy of the Quran) but she can only read from her own memory.
As for your question, the Permanent Committee for Scholarly Research and Ifta’ in Saudi Arabia issued the following fatwa:
There is nothing wrong with menstruating woman or a woman in post-natal bleeding to recite the Quran. This is because there is no clear-cut authentic hadith that forbids them from doing so.
However, Ali ibn Abi Talib reported an authentic hadith which states that; one who is junub (one in a state of impurity following sexual intercourse or wet dream), must not read the Quran while he or she is impure.
The hadith regarding the menstruating woman and the one experiencing post-natal bleeding reads; ‘The menstruating woman and the one who is junub are not to read Quran.’
Ibn Umar reported this hadith, but it is weak. The hadith was reported by Isma`eel Ibn `Ayyash from the Hijaziyeen, and he is famous for narrating weak hadiths from them.
However, such woman (in menstruation or post-natal bleeding) should not touch the mushaf (a copy of the Quran); she can only read from her own memory.
As for the junub, he or she is not to recite the Quran, whether from memory or from the mushaf, until he or she has performed ghusl (major bath).
The difference between them is that the time span for the one who is junub to have himself or herself purified is very short; he or she can do ghusl right away after lovemaking or wet dream.
The junub does not stay in this condition for long, and it is up to him/her when he/she wants to make ghusl. If he/she does not find water, he/she can do tayammum (dry ablution) and then he or she can pray and read the Quran. But the woman in menses or in post-natal bleeding has no control over her situation – the matter is up to Allah the Almighty.
📚 Read Also: Is Purification a Condition for Touching and Reading the Glorious Quran?
Therefore, it is permissible for them to recite the Quran so that they do not forget it and they do not miss learning the teachings of the Shariah from the Book of Allah. If that is the case, then it should certainly be permissible for them to read books containing duaas (supplications) that include verses and hadiths, etc. This is the view believed to be the most correct.
Allah Almighty knows best.