Is it permissible to give zakat to the husband's brother for the purpose of expanding his apartment, knowing that he does not possess the costs of the expansion and is unable to repay the amount?

Zakat is given to the eight categories mentioned in His, the Almighty's, saying: "Indeed, [prescribed] charities are only for the poor and the needy, and those who work on [collecting] them, and those whose hearts are to be reconciled, and for [freeing] captives, and for those in debt, and for the cause of Allah, and for the wayfarer - a duty imposed by Allah. And Allah is Knowing and Wise." It is not permissible to pay Zakat to anyone other than these categories. So, if the aforementioned dwelling does not meet the needs of your husband's brother and his dependents, then it is permissible to give him from Zakat to fulfill this need.