Fiqh-us-Sunnah Volume 3, Zakaat and Fasting, Fiqh 3.010.

Section : Zakah Owed by a Deceased Person.

If a person dies before he pays zakah, then it must be taken from his estate.

According to ash-Shaf’i, Ahmad, Ishaq, and Abu Thaur, it is obligatory that zakah be paid from the property of the deceased, and this payment receives preference over debt, legacy, and inheritance for Allah says: “…after payment of legacies and debts is what you leave…” [an-Nisa’ 12]. Zakah is a debt payable to Allah.

A man came to the Messenger of Allah, upon whom be peace, and said: “My mother died while she still had to make up one month of fasting. Shall I make it up for her?” The Prophet replied: “If there was any debt upon your mother, would you pay it off for her?” The man answered: “Yes.” The Prophet then observed: “A debt to Allah is more deserving to be paid off.” This is related by alBukhari and Muslim.