My father orally gifted the property to my mother in front of witnesses. After my mother's demise, my father is trying to gift the property to my step-brother and register it under his name. Is what my father is doing correct according to the sharia? My father has purchased many properties on my step-brother's name, and he is still a minor. So is that property inheritable? My father is being unjust to us and is giving all his property to my step-brother while he is still alive without considering my sister, who is unmarried, and myself.

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. 

If your mother died without having taken possession of the house that your father gifted to her (by taking full control of it and having the right to dispose of it as she wishes), then the gift is not valid and your father has the right to dispose of the house by selling it, gifting it, or doing any other permissible transaction with it.

However, if he gifts something to one of his children, then he is obliged to gift the same amount to all his other children or withdraw it.

He is not permitted to favor some of his children over others when gifting them unless there is a necessity that requires favoring one child [or some children] over others, such as that child having a chronic disease and so forth, in which case it is permissible to favor him according to his need.

For more benefit, please refer to fataawa 92564 and 89862.

Allaah knows best.