What is the ruling on a brother giving his zakah on wealth to his poor sister?

Zakat is an obligation in Islamic law and the third pillar of Islam. Allah Almighty has specified its recipient in the verse, “Zakah expenditures are only for the poor and for the needy and for those employed to collect [zakah] and for bringing hearts together [for Islam] and for freeing captives [or slaves] and for those in debt and for the cause of Allah and for the [stranded] traveler - an obligation [imposed] by Allah. And Allah is Knowing and Wise” (Quran, 9:60).

Accordingly, Allah Almighty has defined the recipients of zakah, among whom are the poor and the needy — those who cannot secure their daily provision or those who can, but with great difficulty. If the sister referred to in the question cannot secure her daily provision or does so with difficulty, she is eligible to receive zakah; otherwise, it is impermissible.

And Allah Almighty knows best.