Is it permissible for a brother to demand that his sister return part of the money he gave her in exchange for her relinquishing her share of their mother's inheritance, especially after he sold his share of the inheritance for less than expected, knowing that the mother affirmed that the house was a gift to the sons on condition that they give their sisters a certain amount?

The mother is obliged to be just among her children in giving gifts, unless there is a legitimate justification.

The sister's purchase of the air space above her brother's apartment is permissible and legally valid. By doing so, she owns the air space and has the right to dispose of it.

The agreement between the brother and his sister to pay a sum of money in exchange for her right to the air space and what she built therein is a valid contract. The brother cannot revoke it unless the sister grants him rescission.

It does not affect the validity of the contract that the brother intended to sell his share for a larger sum than he actually sold it for, unless he stipulated at the time of the contract that he would not pay the amount unless he sold his share for the larger sum. In this case, if the sale does not occur at the stipulated amount, the contract becomes void, and the air space and what is in it return to the sister, and she returns to her brother the amount she received from him.