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You should tell them that you need viza and to send you Invitation Letter both to you and to Embassy that you will apply for viza.
I think you won't have a problem getting it since they don't make any problems when they see Eurocontrol Invitation Letter.
Tell them to mention in the letter that they will pay for your tickets and accommodation as well.
If the Eurocontrol test is the same as some 10 years ago that is not a test for a ATC Controller it is more a test for someone wanting to become a astronaut or similar,so don't expect too much.
All the best,
Gianni