What is the ruling of Islamic law regarding the division of a deceased father's inheritance, and what is the mother's share of it? What is the ruling on disposing of the summer apartment and completing construction on the rooftop, knowing that the father intended to distribute 5 apartments among his five children and one apartment for himself and his wife, and that the properties are registered solely in the father's name?

What your mother gave to your father is either a complete gift, in which case she is only entitled to the price from his estate. Or it is a partnership, in which case she is a partner in what was purchased, proportionate to her money. The decisive factor in this is your mother's intention at the time of giving the money.

What the father left behind is to be divided among the heirs according to Islamic law. They are not obliged to fulfill what he intended unless they all agree to it while being mature and of sound mind. They may postpone the division of the inheritance for sale or completion of construction and then divide it, or they may divide it as it is now. If one of the heirs wishes to divide it, the other heirs are obliged to fulfill his request.