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May Allah accept – her eligibility is based on whether she would qualify under the categories of the ayah as from al-fuqaraa or al-masakeen – that is, if she lacks the financial resources to meet her most basic needs, OR has basic needs but cannot meet other essential and common needs (which include housing, transportation, etc.). In this case, sources of income such as alimony or child support would be part of the consideration of her access to wealth.
Other special cases include convert sisters or refugees – if this case falls under either, let us know and we can explain in more detail (not all converts or refugees are eligible for Zakat without additional conditions).
If she is eligible, you may give zakat as your intention and she does NOT need to be informed as the recipient – if not, then she would not be Zakat-eligible based on the description.