What is the ruling on a father's action of selling his properties to his son for a nominal price, with the mother acknowledging the right of usufruct for life, and the sisters agreeing to that, and then, after the father's death, the sisters demand that these properties be included in the inheritance?

Favoring some children over others in gifts without a legitimate Shariah reason is an act of injustice and is impermissible. The tricks employed by the father with this intention do not absolve it from being an injustice. The way to rectify this injustice is to return these properties to the inheritance so they can be divided among the heirs according to their Shariah-prescribed shares. As for what was mentioned about the father selling to the mother and the mother selling to you in official documents, these are not real sales due to the absence of all the pillars and conditions of a sale, including the price. Therefore, these assets revert to the inheritance, and each heir takes their rightful Shariah share.