Is it permissible for a daughter to pay Zakat on wealth on behalf of her mother from the debt that the daughter owes her mother, in the event that the mother is stingy and refuses to pay Zakat?

You should encourage your mother to perform the obligation of zakat and gently remind her that withholding zakat out of stinginess is one of the major sins. For whoever is given wealth by Allah and does not pay its zakat, it will be represented to him on the Day of Resurrection as a bald, venomous snake. And no people withheld zakat except that Allah afflicted them with years of drought.

Paying zakat on behalf of your mother without her knowledge is not valid due to the absence of intention, as intention is a condition for obligatory acts of worship. Some scholars, however, have deemed it valid if it is paid from the wealth of the one upon whom zakat is due, permitting it by analogy with the action of an unauthorized agent if approved by the one whose property was dealt with.