ANSWER:

A woman can recite the Qur’an when she’s menstruating, from her memory or from any Tafseer book or her phone or any electronic device.
The prohibition is in touching the actual Qur’an(Mushaf). 

Kindly refer to the following link(s):

https://youtu.be/0g6ttessUcE

Sheikh I have a big confusion some say it is permissible to touch the quaran while a women is menstruating ..Some say it forbidden .. some say it is better to avoid.. am really confused.. please do help me with the same..

Menstruation and post-natal bleeding, Reading/Reciting the Quran | November 20, 2017 7:40 pm
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sheikh, I was in labor from 7am till 5pm in the hospital on the bed with a muscle in my hand etc etc…I couldn’t pray all the prayers that I missed. Should I make up those missed prayers?
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In state of major or minor impurity, what exactly is meant by “Shouldn’t touch the Quran”? Does it mean the pages that contain the sacred text or it includes even the outer hardcover of the Quran which doesn’t contain any sacred text. Is touching the outer cover of the Quran not allowed, to shift it from one place, in state of Junub?