All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
The basic principle is that it is impermissible for the woman to lie in court or elsewhere as lying is prohibited for the Muslim man and woman, as is well-known. However, if the Muslim cannot get his rights through legitimate means and he can only obtain them through lying, then some scholars held that he is given concession to lie in this case as a way of giving precedence to the realization of the hoped benefit over the consequent evil (losing his rights).
We advise this woman to consult the scholars at the Islamic center in her country directly and act upon their fatwa.
Allah knows best.