All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
If the purpose of the authority that set that condition (waiting for six months) is achieved by applying with another email and it does not condition on a person who fails not to apply for another test before the expiry of that period, then there is nothing wrong with what you did. Besides, if the job is in itself permissible and you are able to do the required job as agreed, then you can benefit from the salary given for doing such a job.
It appears according to what is mentioned in the question that the authority does not prevent from applying with another email, unless it conditions on the same candidate not to apply another time. And even if we presume that it conditions this and a candidate applies for a job without cheating and deceit and was permitted to take the test, then this is also permissible as this is with their knowledge and consent. But if it conditions that the candidate should not apply for another test and he changes his name and cheats in order to take the test, then he is not permitted to do so because the Prophet said, “Whoever cheats is not one of us, and cheating and deception are in Hellfire.” [Abu Daawood]
Allaah knows best.