Praise be to Allah.
Yes, it is permissible for her to pray in the entire mosque, but that is on condition that she is not crowded together with men; if it is not possible for her to do that except by crowding together with men, then she should not do it. The ruling concerning the Prophet’s Mosque is that the entire building is the same in terms of reward, and even the extensions that have been added to it come under the same ruling as the original portions in terms of reward. It is proven from the Prophet (blessings and peace of Allah be upon him) that he said: “One prayer in this mosque of mine is better than a thousand prayers offered anywhere else, except al-Masjid al-Haram.” End quote.
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