Answer

In the Name of Allah, Most Gracious, Most Merciful. 

All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.

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In this fatwa:

There is nothing wrong with giving zakah to your needy sister.

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Answering your question, Sheikh Kifah Mustapha, the Imam and Director of The Prayer Center of Orland Park and representative for Dar El Fatwa of Lebanon in the US, states:

Yes, it is permissible to give zakah to needy sisters.

The only recipients that you should not give zakah to are wives, kids and parents. These are your responsibility to care for them even if it will consume all your savings that makes you zakah eligible.

Needy brothers, sisters, aunts, uncles or any person can be a recipient of Zakah.

Almighty Allah knows best.