Is a brother obligated to spend on his sister, and is it permissible to give her from his Zakat?

The brother must spend on his poor sister if he is rich and inherits from her; otherwise, he is not obliged to provide for her, and he may give her from the zakat of his wealth. The conditions for the obligation of spending are that those on whom one spends must be poor, that the one spending has more than his needs, and that the one spending is an heir. If spending on her is obligatory for him, then it is not permissible to give her zakat. But if it is not obligatory, then it is permissible and preferred.