Is it permissible for a mother-in-law to testify before a judge that she acquired properties through a gift, in order to enable the heirs to reclaim their right from their brother who seized a portion of the inheritance, knowing that what was transferred by gift is equivalent to what the brother took, and is this considered as seizing one's right by force (al-Dhafr bi al-Haqq)?

It is not permissible for your mother-in-law to bear false witness that the heirs sold her what was registered in her name through a gift, as this is a forbidden falsehood in Islamic law, and Allah has warned against its perpetrators. It is not known whether what was registered for her is equal to her husband's share. Her husband can claim his right through legitimate means, including appealing to the competent authorities or consulting with scholars.