Thank you!
I bought my Student license with Premier Service. After payment was succesful, I downloaded Mathematica and installed it on my PC (self-built highend desktop, Win 8.1 Pro), then I activated it via online activation and registered it in the Wolfram User Portal.
Then, I used a USB drive to get the downloaded Mathematica zip folder on my notebook (Lenovo Thinkpad X1 Carbon, Win 7 Pro), and installed it, which was succesful - but activation failed, because the system doesn't accept my activation key. What tho do now? As the description of Premier Service says, it's possible to install Mathematica on a second system, so the key should be accepted?
Another strange fact is that in my User Portal the box with "summary of benefits" - when you go to "My Produts and Sercives", click Mathematica and "Premier Service" - is empty?!