Does prepayment of Zakah on livestock that subsequently multiply to a full Nisab suffice if the original stock perishes and a full Hawl passes on the offspring?

Primary text

If Zakah is prepaid for a full Nisab of livestock, and that stock subsequently multiplies to a new full Nisab, while the original stock dies and a Hawl (full lunar year) passes on the offspring, the prepaid amount suffices for the offspring. This is because the offspring entered the Hawl of the original stock and stand in its place, thus discharging the Zakah liability for them. This applies specifically when forty sheep are owned, one sheep is prepaid, and forty lambs are born, the mothers die, and the Hawl passes on the lambs; the prepaid offering is sufficient.