All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
If the situation is as mentioned in the question that the husband gifted the jewellery set to his wife, then it becomes her property and her father-in-law has no right to keep it without her permission. She is the one who can use it as she pleases: she can sell it, gift it and the like, if she is mature and has sound judgement. So the father-in-law is obliged to fear Allaah and he should know that he has no right to prevent his daughter-in-law from taking her wealth and making use of it.
As regards lying to him so that she would take back her right from him, in principle it is forbidden to lie, however, if it is not possible for her to obtain her right by tricking and using Tawriyah (saying something which has more than one meaning and intending a meaning different from what the listener is likely to understand), and there is no other alternative than lying in order to obtain her right, then she may do so.
Allaah Knows best.