As soon as a person dies, his wealth is transferred to his heirs. Thus financial obligations are transferred from the original owner of the wealth (the father who left it behind) to the new owners (the heirs). After having been the property of one person, it is now divided among the heirs according to their shares of inheritance. The mother gets one-eighth of the estate and the rest of it is divided among the children, with each male getting the share of two females.
Each of them then adds the wealth that he or she has inherited to his or her previous wealth, if applicable. Based on that, each one of them will have a nisaab [minimum threshold] independent of the others. The year for the inherited wealth (after the passage of which zakaah becomes due) begins when the person who left this estate behind dies and the wealth is transferred to the heirs. If he died before zakaah on his wealth became due, this year no longer counts and a new year begins for the heirs.
The scholars of the Standing Committee were asked:
When should the heir pay zakaah? Is it when he takes possession (of the inheritance) or after one year has passed since he acquired it? And what about in the case a gift, if it is in the form of cash or real estate?
Zakaah must be paid on the estate when one year has passed since the death of the one who left it behind, because ownership of the estate passes from the deceased to the heirs on the date of death, if the heir’s share reaches a minimum threshold (nisaab) of cash or gold or silver jewellery.
End quote from Fataawa al-Lajnah ad-Daa’imah, 9/305
If the estate includes agricultural land, then the heirs must pay the zakaah on the produce on the day of harvest; it is not permissible to delay it until one year has passed, because Allah says (interpretation of the meaning): “but pay the due thereof (its Zakat) on the day of its harvest” [al-An‘aam 6:141].
The returns on the agricultural land that yields produce come under the same rulings as the original estate: they are to be divided according to the shares of each one, with each male getting the share of two females. But zakaah must be paid for the entire yield before it is shared out among the heirs.
With regard to zakaah on the houses: if they are intended for living in, then no zakaah is due on them at all.
If they are intended to be rented out, there is no zakaah on the houses themselves, but zakaah must be paid on the rent, which should be added to the rest of the wealth and zakaah should be paid on it if it reaches the minimum threshold and one year has passed.
See the answer to question no. 159321
If you did not pay zakaah for the previous period, from the date of your father’s death, then you have to pay it as described above. In that case you will be responsible for paying the zakaah of one year, and at the end of the second year, of which half has passed, you have to pay zakaah for that year too.
And Allah knows best.