Is it permissible to make a will in favor of an heir within the limit of one-third, or is it not permissible for him to make a will at all?

A will in favor of an heir is not permissible, due to the Prophet's (peace and blessings be upon him) saying: "Indeed, Allah has given every rightful person his due, so there is no will for an heir." This is by agreement of the four Madhhabs.

However, if a person makes a will [in favor of an heir], it is not valid unless the adult heirs permit it after the death of the testator.

If some heirs permit it and others do not, the will becomes effective in the share of those who permitted it, but not in the share of others.