Praise be to Allah.
Mahr in Islam
Mahr is one of the rights of the wife, which is hers to take in total and is lawful for her, in contrast to the widespread practice in some countries, where the wife is given no dowry.
Evidence for the permissibility of taking the mahr
Evidence that the wife must be given her dowry is found in many places, for example the verse (interpretation of the meaning): “And give to the women (whom you marry) their mahr (obligatory bridal money given by the husband to his wife at the time of marriage) with a good heart…” [al-Nisa 4:4]
Ibn 'Abbas said: “This refers to the mahr (dowry).”
Ibn Kathir, may Allah have mercy on him, said, summarizing the comments of the mufassirin on this verse: “The man must definitely pay the dowry to the woman, and he should not resent it.”
Allah says (interpretation of the meaning): “But if you intend to replace a wife by another and you have given one of them a cantar (of gold, i.e., a great amount) as mahr, take not the least bit of it back; would you take it wrongfully without a right and (with) a manifest sin? And how could you take it (back) when you have gone in unto each other, and they have taken from you a firm and strong covenant?” [al-Nisa 4:20-21]
Ibn Kathir, may Allah have mercy on him, said:
“This means: if any one of you wants to divorce his wife and replace her with another, you should not take anything from what you have already given the first wife, even if it was a huge amount of wealth. The mahr is given in exchange for the right to enjoy marital relations. For this reason Allah says (interpretation of the meaning): “And how could you take it (back) when you have gone in unto each other…?” The “firm and strong covenant” is the marriage contract.
Anas ibn Malik, may Allah be pleased with him, reported that ‘Abd al-Rahman ibn ‘Awf came to the Messenger of Allah (peace and blessings of Allah be upon him), and there were traces of yellow (perfume) on him. The Messenger of Allah (peace and blessings of Allah be upon him) asked him about it, and he told him that he had just married a woman of the Ansar. The Prophet (peace and blessings of Allah be upon him) asked him, “How much did you give her?” He said: “Gold equal to the weight of one date stone.” The Messenger of Allah (peace and blessings of Allah be upon him) said: “Give a walimah (wedding feast) even if only with one sheep.” (Reported by al-Bukhari, 4756)
Can the father take the mahr without the wife’s approval?
The mahr is the right of the wife, and it is not permitted for her father or anyone else to take it except with her approval. Abu Salih said: “When a man married off his daughter, he would take her mahr away from her, but Allah forbade them to do that, and gave women the right to the mahr they received.” (Tafsir Ibn Kathir)
Can the wife forgo any part of the mahr?
Similarly, if the wife foregoes any part of the mahr , the husband is permitted to take it, as Allah says (interpretation of the meaning): “… but if they, of their own good pleasure, remit any part of it, take it, and enjoy it without fear of any harm (as Allah has made it lawful).” [al-Nisa 4:4]
For more about mahr, please see these answers: 10525 , 94880 , 93780 , 185602 , and 102507 .
And Allah knows best.