What is the ruling on buying a bottle of perfume containing alcohol for a relative who believes in the purity of alcohol and the permissibility of its use in fragrances, and does the impurity of alcohol remain even after its evaporation?

The preponderant view is that alcohol is impure, and perfumes containing it are also impure. However, this is a valid matter of scholarly disagreement. If you believe alcohol is pure, or you follow a scholar who holds this view, then there is no sin upon you in buying perfume for this person. But if you believe it is impure, or you follow a scholar who holds this view, then it is not permissible for you to buy it, because by doing so you would be assisting him in what you believe to be a sin.