Is the apartment inherited from the father—for which the mother paid the installments with nothing written down—to be divided as an inheritance, or is it considered jointly owned by the heirs?

Lease-to-own contracts can be valid or invalid. If the contract is invalid, the apartment does not belong to the heirs because the deceased never truly owned it. What was received under an invalid contract must be returned to its original owner, and the leasing entity is entitled to receive the fair rental value for the duration of the occupancy. If the contract is valid, the apartment belongs to the heirs after the death of the deceased, and the installments remain a debt upon the estate. The selling entity or whoever paid the installments (unless it was a donation) has the right to claim their due from the apartment.