Is it permissible for women to pray in a Qur'an memorization center located above a mosque, given the disagreement as to whether it is considered part of the mosque, and is it permissible for them to pray in congregation in this place at the same time as the men's prayer downstairs?

If a mosque is built on endowed land, then everything above it is considered part of it, and it is not permissible to build residential units above it. However, if the mosque is part of an existing structure, such as converting a lower floor into a mosque, then the upper floors retain their original ownership. If a Quran memorization office is affiliated with the mosque and built on its endowed land, women can pray there, following the Imam, even if they do not see the Imam or the congregants, provided that the sound reaches them. But if the mosque was established after the office was built, or if the endower intended to build offices and apartments above it, then what is above the mosque is not considered part of it and does not take its ruling. In this case, women should not pray there, following the Imam, unless the women's section in the mosque is full and the rows are connected. Women in a separate area can pray in congregation among themselves.