Is it permissible to give a poor brother whose income is insufficient money from Zakat to help him with a business project?

We commend the questioner for his eagerness to disburse zakat to its rightful recipients. It should be clarified that the brother is not eligible for zakat if he is able to earn a living, based on the Prophet's (peace be upon him) saying: "There is no share in it [zakat] for the rich, nor for the strong, able-bodied earner." If he is unable to earn a living, and his mother is wealthy, then his maintenance is her responsibility. If he is self-sufficient due to her support, then zakat is not permissible for him. The mother can give him money to earn a livelihood, and the questioner can assist her out of piety and maintaining kinship ties, but it is not permissible to disburse zakat money to him.