Is it permissible to give zakat to a sister whose husband has limited income and who suffers from a chronic illness, even though her mother bought her an apartment and she receives monthly financial assistance that does not cover her needs?

It is permissible to give the poor sister from the Zakat, and she has more right to it than others; because it is both charity and strengthening kinship ties. It is stipulated that the questioner is not an heir to her sister. If she is an heir to her, then providing for her is obligatory upon her, and it is not valid to give Zakat to someone whose maintenance is obligatory upon the giver.