Is it permissible for my grandmother, to whom a house was gifted in her name, to bequeath half of it to my paternal cousin whose father has passed away, and deprive my maternal cousin whose mother has passed away from his mother’s inheritance, under the pretext that my father contributed to the construction of the house?

If the grandfather wrote the house to his grandmother, then it is hers to dispose of during her lifetime. After her death, it will go to her heirs after her debts are paid and her will is executed.

The daughter's son is not an heir, while the son's son is an heir unless he is excluded by the presence of a direct living son of the grandmother. If the grandmother wishes to gift half of the house to her son's son, then he must own it and have the right to dispose of it. The grandmother is not required to be equitable among her grandchildren in gifting.

If the grandmother wrote half of the house to the son's son but did not grant him the power to dispose of it, then it is considered a will. A will to an heir is not permissible, nor is it permissible for more than one-third of the estate. If the son's son is excluded, then a will for him up to one-third of the estate is permissible, provided that half of the house does not exceed one-third of the estate. However, if the son's son is not excluded, then a will for him is not permissible. If the grandmother makes a prohibited will, the will is valid but contingent upon the heirs' approval.