Is it permissible for a Muslim to buy a house from a non-Muslim investor who legally purchased and owned it, and then sold it to the Muslim for a deferred price with profit, or must the sale be conducted through an Islamic bank?

For the permissibility of a Murabahah sale to one who requests a purchase, it is a condition that the bank or company genuinely owns the house and takes possession of it before selling it to the client. It is not a condition for the contracting party to be an Islamic bank, and it is permissible to deal with a non-Muslim investor if the Shariah conditions are met; because there is no harm in dealing with disbelievers in buying and selling, and this is not considered the forbidden form of allegiance. Indeed, the Prophet, peace and blessings be upon him, bought from a polytheist and a Jew.