Does the husband have the right, Islamically, to reclaim a gold necklace that his mother gifted to his wife on their wedding day, given that the wife was divorced after three years and the husband is now demanding its return, claiming it is an inheritance, even though the law does not permit him to do so?

A gift is not binding until it is taken possession of. It is forbidden to revoke it except in two cases: a father revoking what he gifted to his child, and one who gifted something for a specific purpose which was not fulfilled (a gift of reward). If a mother gifted a necklace to her son's wife for a specific purpose, such as good companionship, and that purpose was fulfilled for a sufficient period, then she is not allowed to revoke it. Nor is the son allowed to revoke it after his mother's death.