Does divorce occur without the payment of the mahr, knowing that the husband has procrastinated in paying and wants the wife to seek divorce so that he does not have to pay her dues? And is it permissible to file a lawsuit against him?

If the dower (mahr) was specified before consummation and the husband wishes to divorce, he must pay half of the named dower, unless the woman or her guardian waives it. However, if the dower was not specified, she is only entitled to a consolation gift (mut'ah) according to the husband's financial situation, and she has no right to maintenance unless he has consummated the marriage or had a valid seclusion (khalwah sahihah) with her.

If he has consummated the marriage or had a valid seclusion with her and then divorces her, she is entitled to the full named dower, or the dower of her peers (mahr al-mithl) if it was not specified, in addition to her maintenance from the time she made herself available to him until the time of divorce. It is not permissible for him to leave her in suspension; rather, it is either retaining her honorably or releasing her kindly. She has the right to refer the matter to the Sharia court.