All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The appropriate thing to do, first of all, is to look into the ownership of this estate by its original owner. In principle, it belongs to that person as long as it has not been established that he gifted it to your mother. If this estate was his possession, it becomes the possession of his heirs. Abu Hurayrah narrated that the Prophet said: "... and whoever leaves any wealth, it is for his heirs.” [Al-Bukhari and Muslim]
If we presume that he gifted it to your mother in a valid way, and she became the owner, then it is not permissible for her to favor any of her children with a gift over others unless there is a legitimate reason for doing so. Ibn Qudaamah from the Hanbali school of jurisprudence, said: “Favoring some children over others with gifts for a reason that requires such particularization, such as a having a particular need or chronic health condition, or being blind, or having many children, or acquiring Islamic knowledge or other virtues, then quotes from Ahmad indicate that this is permissible.”
Accordingly, if there was any reason for specification, like in the case of this physically challenged person, then the gift is valid. Otherwise, the gift is part of the inheritance of your mother and should thus be divided among her heirs according to the Sharee’ah. If there is a dispute over this, then it is better to take the matter to the authorities that are specialized in examining Muslim affairs.
Finally, it should be noted that adoption is forbidden and the laws that apply to actual children do not apply to adopted children. Such laws include financial support, inheritance and legal prohibition of marriage. For more benefit, please refer to Fataawa 82371 and 117371.
Allaah Knows best.