What is the description of a wife’s denial of her actual dowry (furniture, gold, and money) and her returning only the nominal dowry? Is this considered a breach of trust or perjury, or does it have another description? And in this case, does the wife remain lawfully married to her husband because she has not ransomed herself, as stated in the Book of Allah?

The legitimacy of khul' (divorce at the instance of the wife) is established by the Quran and Sunnah (definition), and it is recommended for the husband to assent to his wife's request for it. The consideration for the mahr (dower) is what the two parties agreed upon at the time of the contract, not what is written formally. So, if the khul' takes place based on the mahr, it is incumbent upon the wife to pay the real mahr, and if she denies it, that is a lie and a betrayal. It is not a condition for khul' to be based on thehr; rather, it is based on whatever they agree upon. The validity of khul' does not stipulate the actual receipt of the compensation. So, if she divorces him by khul' in exchange for the mahr and does not pay it in full, the khul' is valid, and the mahr becomes a debt upon her.