What should we do with the remaining amount of the dowry after the former husband refused to receive it, and is it necessary to inform the new suitor about this money?

If a woman is divorced before consummation and before valid seclusion, she is entitled to half of the named mahr (dowry), both its immediate and deferred portions. This is based on the Almighty’s saying: "And if you divorce them before you have touched them and you have already specified for them an obligation (mahr), then for them is half of what you specified – unless they forego it or he forgoes it in whose hand is the marriage tie." (Quran 2:237)

Furthermore, she is not required to observe an 'iddah (waiting period), based on the Almighty’s saying: "O you who have believed, when you marry believing women and then divorce them before you have touched them, then there is not for you any 'iddah to count concerning them. So provide for them and release them with a gracious release." (Quran 33:49)

As for the 'shabka' (engagement gift/jewelry), if it is customarily considered part of the mahr, it is divided accordingly. If it is a gift, it belongs to the wife. It is commendable to waive the half that is due to the other party, as the Almighty says: "And that you pardon is nearer to righteousness. And do not forget graciousness between you." (Quran 2:237)

If the husband does not agree to take his due, it can be kept as a trust or handed over to the court.