What is the religious ruling regarding the deceased's properties that were registered in the name of his younger half-sister, and what is the ruling regarding the wife's relationship with her sister and mother after this discovery?

A father must be equitable among his children in giving gifts. If he favors some of them without a valid reason, he commits a sin and must repent by returning what he favored or by giving the others their due share. If the father dies before rectifying his injustice:

1. If the gift was given while he was healthy: It is valid, and the heirs are called upon to be equitable, or the heirs may reclaim what he gifted. 2. If the gift was given during his death illness (marad al-mawt): It is not effective, and the inheritance must be re-divided according to Islamic law.

If the deed was written in the name of the youngest sister without possession (haza) during the donor's lifetime, it is considered a bequest to an heir (wasiyya li-warith) and is not valid unless approved by the rest of the adult heirs; otherwise, it must be returned to the estate.

The wife must maintain kinship ties with her sister and be kind to her sister's mother (her stepmother).

Given the existence of a dispute, the matter should be referred to the Sharia court or presented to scholars.