Is it permissible to sell a property inherited by sons from their father, knowing that there is a mosque beneath it, and will the mosque remain a mosque after the sale, given the concern that the buyer might not adhere to the condition of not closing the mosque?

If a person builds a mosque and declares it an endowment (waqf), or authorizes the call to prayer (adhan) in it, it becomes an endowment and ceases to be his property. Its sale becomes prohibited, based on the hadith of Umar ibn al-Khattab, may Allah be pleased with him, regarding the dedication of his land and donating its produce. An endowment is a binding contract merely by declaration, and it is not permissible to revoke or sell it unless its benefits are entirely lost.

Therefore, if you wish to sell the building that has a mosque beneath it, the contract must explicitly state that the sold building does not include the mosque, and that the mosque is an endowment for Allah Almighty. You may stipulate supervision over the endowment or appoint someone to supervise it. If the buyer refuses to exclude the mosque, then the solution is to sell the apartments one by one.