Originally, the dowry (or more correctly, dower) or mahr is the right of the wife and it should be given to her. However, if the proposing man gave the mahr to the woman’s father, then there is nothing wrong in that and the father should give it to the bride.
Dr. Muzammil Siddiqi, former president of the Islamic Society of North America, states in this regard that: “Mahr is a wife’s right, which becomes binding upon the husband once the marriage is contracted. It is fully payable after the consummation of marriage. Allah says in the Qur’an, “And give women (on marriage) their dowry as a free gift; but if they, of their own good pleasure, remit any part of it to you, take it and enjoy it with right good cheer.” (Al-Nisa’ :4)
Mahr is very important in Islamic marriage. It is obligatory on the husband to pay mahr to his wife unless she expressly, by her own will and without any pressure, tells her husband that he does not have to pay it, or she returns the amount of mahr to him. Mahr belongs to the wife and it is to be given to her only. It is not the property of her parents or her guardian. No one can forgive the husband to pay the mahr except the wife herself; or in case she did not go to her husband and the marriage ended without consummation, then in that situation her guardian can also forgive the mahr on her behalf.

Stressing the fact that mahr is the wife’s pure right and the fact that she is originally entitled to receive it, Dr. `Ali Juma`ah, professor of Principles of Islamic Jurisprudence, adds: Usually, the money that is paid by the husband to the wife upon the consummation of marriage is known as mahr. It is totally the right of the wife and the woman’s father is not entitled to it in the first place. The woman is the owner of mahr and it should be given to her.
however, if the proposing man gave the mahr to the woman’s father, then there is nothing wrong in doing that, and in this case, I urge the father of the bride to give his daughter the mahr afterwards, as it is her right, whether it is paid in advance or deferred.
Referring to the fact that women are entitled to their mahr and the fact that it should be originally given to them not their fathers, Allah Almighty says: “And give women (on marriage) their dowry as a free gift… “” (Al-Nisaa’ :4)