Praise be to Allah
It is obligatory to take care of ties of kinship, and not to sever them when family disputes arise, because severing ties of kinship is a major sin.
If a man has prepared the zakaah of his wealth, then it is stolen or destroyed, he must give it again, because the zakaah did not reach those who are entitled to it. See the answer to question no. 159996.
If the owner of the wealth delegates someone else to give his zakaah, the person whom he appoints is his deputy and is acting on behalf of the owner of the wealth.
If the zakaah is stolen from him or is destroyed, the owner of the wealth must give it again, because his deputy was acting in his stead, so it is as if it was stolen from him or was destroyed when it was in his possession.
An-Nawawi (may Allah have mercy on him) said:
Chapter on giving zakaah:
Zakaah is obligatory with immediate effect, once one is able to give it (after his wealth reaches the nisaab and one full year has passed), then to pay it, he has to form the intention and take action. As for taking action it, this may be done in three ways:
i. The owner distributes it himself, which is permissible
ii. He delegates that to the ruler (the authorities), which is permissible
iii. He appoints someone else to deliver it to the ruler (the authorities) or to distribute it among the categories of people for whom it is permissible for him to distribute it himself.
As for which of these ways is better, distributing it himself is better than appointing someone else to do it, with no difference of opinion among the scholars concerning that, because the person appointed to do it may betray that trust, in which case the obligation is not waived from the one who appointed him.
End quote from Rawdat at-Taabieen (2/204-205)
Al-Bahooti said in Kashshaaf al-Qinaa‘ (2/268):
If the zakaah is destroyed when it is in the possession of the person appointed by the owner of the wealth before he has delivered it, then the owner of the wealth is still liable for it, because he has not fulfilled what he was enjoined to do (of ensuring that it reaches the poor), and because the hand of the deputy is like the hand of the one who appointed him to do that task.
See also the answer to question no. 36512.
Based on that, if your husband appointed his sister to give the zakaah and she did not do it, and did not deliver it to the people who were entitled to it, then he must give it again.
What he must do now is give the zakaah of his wealth for one year only, which is the year that has already passed. As for the wealth that he wanted to give for the coming year, he does not have to give anything else instead of it at present; rather he should wait, then when the year has passed, he should see what he has to give of zakaah on his wealth, and then give it.
We ask Allah to set things straight among you, and to reconcile between the brother and his sister, and to restore to people what is due to them.
And Allah knows best.