Zakat should be given to an eligible person without any condition and with full ownership, so that they can use it according to their own needs. Therefore, even if the giver tells the eligible person how the zakat must be spent when handing it to them directly, they are not bound to spend it that way once they have received the zakat money with full ownership.
It is therefore better to give the zakat money to the eligible person unconditionally, into their ownership, so that they can spend it according to their needs. However, if they choose to spend it on paying off their debt, that is also correct.
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دلائل:
الدر المختار مع رد المحتار: (345/2، ط: دار الفکر)
لأن الحيلة أن يتصدق على الفقير ثم يأمره بفعل هذه الأشياء وهل له أن يخالف أمره؟ لم أره والظاهر نعم
(قوله: والظاهر نعم) البحث لصاحب النهر وقال؛ لأنه مقتضى صحة التمليك قال الرحمتي: والظاهر أنه لا شبهة فيه؛ لأن ملكه إياه عن زكاة ماله وشرط عليه شرطا فاسدا والهبة والصدقة لا يفسدان بالشرط الفاسد.
Allah the Almighty knows best.
Darul Ifta Al-Ikhlas, Karachi.