Answer
(Fatwa: 1733/L1100/L=1433)
If your sister is the owner of those jewelleries then its zakah is wajib on your sister. She shall be sinful in case zakah is not paid. As salah is fardh on your sister and it is necessary on your sister to offer it, in the same way if zakah is fardh on your sister then it is necessary on your sister to pay it. If she does not have money then she should sell some jewellery and pay zakah. It is not necessary on husband to pay the zakah of wife’s jewelleries. However, if the husband pays it with the permission of wife then zakah shall be paid.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband