For my marriage my father paid the Mahr (Assadaqa) for me. Do I have to give my father the amount he paid for the Mahr as soon as possible or not? He doesn't expect that, but I want to know if according to Sharia if the Mahr must be paid by the husband to his wife or carry other person can do it for him?.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Mahr (bridal gift) is an absolute right of the wife upon her husband. So, he is obliged to pay it to her. However, there is no harm if one pays the Mahr on behalf of the husband. Thus, he becomes free from this obligation.

Paying the Mahr from the husband's own money is not mandatory. If the amount of Mahr paid by your father was a loan, then it is a debt that you have to pay him back whenever you are able to pay it, but if he gave it to you as a gift, then you are no longer responsible for it.

Allah knows best.