Is it permissible for the mediator to set the value of the deferred dower ( مؤخر الصداق) at less than the amount agreed upon in the contract, with the consent of the divorced woman's guardian? And is it permissible for the divorced man to pay the remaining amount after the divorce is finalized?

There is no objection to a reconciler between divorced spouses ruling that the woman waive part of her mahr, as long as she is content, for the mahr is her exclusive right, as Almighty Allah says: {And give women their mahr as a free gift. But if they are pleased to remit to you a part thereof, consume it with good cheer and satisfaction.}

If the divorced woman authorizes her father or someone else to absolve part of the deferred mahr, or if she entrusts him with estimating that part, then the absolution is valid, and the divorcing husband's obligation is discharged upon payment of the remaining deferred amount.

Therefore, if it is established that the divorced woman authorized her father, then the divorcing husband's obligation is discharged by paying the amount requested by the agent, and he is not obligated to pay the rest of the deferred amount. If the husband wishes to be more scrupulous and pay the remaining amount, there is no objection, but it is preferable to verify with the divorced woman or her guardian that her right has been fully received.