[Do the Heirs Build on the Deceased’s Zakat Year?]

Answer: Each of the two sons must pay one sheep when a year has passed over the flock—that is, when a full lunar year has elapsed from the day their father died. They are not obliged to pay zakat on the flock at the zakat date their father used to pay for that flock, for the father’s zakat year was cut off by his death, and the flock passed into the ownership of others.
Source : Min Thimār al-ʿIlm wa al-Ḥikmah vol.1