What is the ruling regarding the old mosque next to which a new mosque has been built? Is it permissible to sell it, or designate it as a prayer area for women and a Quran memorization center, or convert part of it for services, or pray in it permanently while the new mosque is designated for Friday prayers and Eid prayers?

If a mosque is built and people are enabled to pray in it, it becomes an endowment (waqf) for Allah Almighty. It is then forbidden to sell it, exchange it, or relocate it. If the old mosque can be utilized as a prayer hall for obligatory prayers, a Quran memorization center, or similar, then it should be left as is. However, if it cannot be utilized as a mosque, then it is permissible to move it to another location.