Is the first husband entitled to half of the agreed-upon mahr if he divorces his wife after falsely accusing her, knowing that he did not claim it after the divorce?

Firstly: A husband slandering his wife and accusing her honor is one of the gravest sins, necessitating punishment and the rejection of his testimony, unless he produces lawful evidence or performs li'an, based on the Almighty's saying: (And those who accuse chaste women and then do not produce four witnesses - lash them with eighty lashes and never accept their testimony thereafter. And those are the defiantly disobedient) [Quran 24:4].

Secondly: A husband pressuring his wife by falsely accusing her, harming her, and beating her to make her give up her mahr or part of it is called "'adl" (coercion), and it is forbidden unless she commits a clear act of immorality. In this case, what the husband takes is unlawful and forbidden if he is lying and unjust. If he is truthful, then he must prove it with four witnesses or by performing li'an.

Thirdly: The husband has no right to half of the mahr he stipulated, because he did not bring witnesses for what he accused her of, nor did he perform li'an, nor did he see anything that would make him guiltless. The right belongs to the wife.