Is it permissible to purchase an apartment for residential purposes from a fund affiliated with one's employer, operating on the principle of Islamic Murabaha, where the fund buys the apartment and then sells it to the employee in installments, with the apartment mortgaged to the fund until the full price is paid?

There is no objection to the aforementioned transaction if the fund purchases the apartment and takes possession of it, then sells it to the employee. This falls under the category of Murabaha sale to a party requesting a purchase. There is no objection to mortgaging the apartment to the fund until the employee pays its full price, to ensure it is not sold. It is permissible to stipulate mortgaging the sold item against its price. The sold item becomes the property of the employee as soon as he purchases it, and no longer remains the property of the fund.