Will the sister who died after her father but before her mother inherit from her father's properties that he wrote to the deceased's mother? And is the father sinful for writing all his properties to the deceased's mother?

The legal ruling regarding a father selling his properties to his wife can be summarized in two possibilities:

1. Valid Sale: If the sale was a genuine transaction conducted during the father's lifetime and while he was in good health, then the properties belong to the wife. If there remains a debt owed to the wife from the price of these properties, it must be added to the father's estate to be distributed among the heirs, including the daughter who passed away after him.

2. Fictitious Sale: Gift (Hibah): If the father intended a gift and to transfer ownership of all his assets to his wife while he was in good health, then this is a valid gift if the wife took possession of the properties. The intention to disinherit heirs does not invalidate the gift, but the father incurs sin by intending such. Bequest (Wasiyyah): If the father intended by the fictitious sale a bequest to his wife of all his wealth after his death, then this bequest is invalid because it is for an heir, according to the Prophet Muhammad, peace be upon him, who said: "There is no bequest for an heir." In this case, what the father left behind is considered an estate to be divided among all the legal heirs, including the daughter who passed away after him, and her share is then divided among her heirs.

Given the complexity of the matter, it is recommended to refer it to the Sharia courts for a ruling.