As i said before, your cousin was banned for impersonating so his UID( laptop ) was blocked. You could ask him to post unban appeal if he/you want us to allow the UID to join the server again. He broke the rules and crack banned him, he is the one that is responsible for his UID( his laptop ) and his action.
There's nothing more you or us could add here. It's already clear that he was banned for impersonating and you cant use his laptop until he get unbanned. There is nothing wrong with the ban as he really broke the rules using his laptop. You could PM Crack and discuss with him or tell your cousin to post unban appeal. It's up to the admin that banned him.