Hi,
if you registered yourself, and this is an "officiel way" to register (I don't know if it is) - then Borgerservice can see in their IT-systems that you are registered.
In relation to A-kasse it is not necessary the date of registration at Borgerservice which is important - what the rules say is that you must have a permanent address in Denmark no later than one day before the start of your education.
I am not sure how the A-kasse determine if you have the permanent address before you started education - but you need to contact your A-kasse and they will be able to tell whats important and how you has to proove that you were in Denmark before you started your education.
Best regards,
Anders, www.a-kasser.dk
