There are two main ways of properly presenting mahr to the bride.
The first way is to hand it over in full at the time of marriage, in which case it is known as mahr mu'ajjal, or 'promptly given mahr'. (Notice the ' . The word is derived from 'ajilah, meaning 'without delay'. This was the accepted practice during the time of the Prophet, and the amount fixed was generally quite minimal.
In the case of Fatimah and Ali, Ali informed the Prophet that he had nothing to give her. The Prophet reminded him of a coat of chain-mail he had been given. It was still in his possession, although in a dilapidated condition and worth less than four dirhams. The Prophet suggested he gave that to Fatimah, and this was done.
The second way of presenting mahr is to defer it, to hand it over to the bride after a certain period of time, the duration of which must be specified, fixed by the man and agreed by the wife. This has to be settled, with witnesses, at the time of the marriage. This form of mahr is known as mahr muwajjal. (the word implies 'in a period of time').
The five major schools of Islamic jurisprudence all agree that delay in handing over the mahr, whether in full or in part, is lawful provided that the fixed period for payment is not indefinite.
This method should never be used as an excuse to willfully postpone the payment. A definite date should always be fixed, witnessed, and adhered to. It should certainly not be left 'hanging' in case the marriage breaks down and the couple come to consider a divorce - because of the inevitable emotions, bitterness, arguments, hostilities and financial problems involved at that time.
If the husband died, or they got divorced, the mahr debt must be paid up immediately to the widow before his inheritance or other financial settlements are considered. It is her property, and not his.
Repayment of Mahr in cases of khul divorce.
A khul divorce is one in which a wife sues for divorce even though the husband has not driven her to it by his unreasonable behavior.
If there is no good reason for a wife wishing to divorce her husband, but it is a case in which she simply wishes to finish the marriage with no particular legal grounds against the husband, the husband may agree to grant her the divorce if she returns all or part of the mahr. This has to be agreed between them.
If the wife does have genuine grounds for divorce - such as cruelty, mental cruelty, breaking of the marriage contract, adultery, desertion, incurable insanity, long-term imprisonment, abandonment of Islam - then the divorce is not khul but a normal talaq, in which the wife has as much right to instigate proceedings as the husband. In these cases, she most certainly does not have to hand over any of the mahr.
If the wife has genuine grounds for divorce but the husband refuses the divorce, she may then approach lawyers for khul, and appoint an Imam to act for her. It is sensible to do this as well as having a UK lawyer. She is not required to pay back any of her mahr. Indeed, the lawyers may demand some further compensation for her if the husband is guilty. (She may have to prove his guilt, and should gather as much evidence beforehand as she can - such as signed and witnessed statements of witnesses, photographs of injuries sustained, etc).