What is the way to solve the problem of an engagement after a lie caused the relationship between the fiancé and the fiancée's brother to be ruined, knowing that the fiancé does not want to respond to the lie in order to avert harm from others?

If a man has lied to you to sow discord between you and your wife's brother, he has committed a great sin by combining slander and backbiting, both of which are major sins. As for your wife's brother, he erred by not verifying the news. Both of them must repent. You have the right to defend yourself and clarify the truth, but it is not permissible for you to lie to him as he lied to you, nor to harm someone who has no connection to the matter.