Is it permissible to hack a girl’s account and close it to prevent a brother from becoming attached to her, given the deterioration of his psychological state due to her not responding to him and his current inability to marry her?

Hacking websites and accounts is prohibited and unlawful because it constitutes an infringement upon the rights of others. What was mentioned is not a justification for permitting the hacking of an account or trespassing upon it. You must advise your brother and guide him to act according to what is stated in the fatwa regarding the cure for infatuation.