What is the ruling on Zakat from the estate of a man who informed his heirs that he had not paid it throughout his life? And is it obligatory for them to pay it on his behalf to alleviate the punishment from him, and for how long a period should it be paid?

As long as the man in question claimed to have paid Zakat, this is sufficient, and the heirs are not required to pay it merely based on their suspicion. The default is to believe a Muslim. However, if it is proven that he did not pay it, then scholars have differed on whether it should be paid from the inheritance:

1. The Shafi’is and Hanbalis hold that financial debts owed to Allah (such as Zakat, expiations, and Hajj) must be paid from the inheritance, basing their argument on the hadith: "The debt owed to Allah has more right to be fulfilled." 2. The Hanafis are of the view that death nullifies the debt owed to Allah if the deceased did not make a will concerning it, and thus it should not be taken from his inheritance, because a debt owed to Allah is an act of worship that requires the intention and action of the obligated person. 3. The general principle among the Malikis is that death nullifies debts owed to Allah, except in three cases: if he bequeathed it in his will, or if he bore witness during his lifetime that it was an obligation upon him, or if it was related to an existing asset, such as Zakat on crops and livestock.

If the heirs wish to pay the Zakat as a precaution, out of concern for their deceased, this is considered a voluntary donation from them, and it should only be paid from the share of the adult and mature heir.