Is zakat due on an inherited sum of money if its zakat has not been paid previously, and how is it calculated if the duration of its possession is unknown, and is it permissible to give it to the sick husband of one's sister if the sister has already received her share of the inheritance?

The heirs must pay zakat (definition) on the wealth for the years they are certain that the wealth reached the nisab (definition) and a hawl (full lunar year) passed on it. As for the years they are unsure about, it is more cautious to pay zakat for them if all heirs are adult and رشيد (of sound mind). Otherwise, the disputed zakat should not be taken from the share of the one who is not رشيد. There is no objection to giving zakat to the sister's husband if he is deserving, and this has no bearing on the sister taking her share of the inheritance.