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Choose "JetBrains account" option if you see your license in your JB account (available at ).Maybe you have not received such email yet.
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When you say "My history says that I have a purchase, sent an invitation to myself, accepted this and to now login to my account within PHPStorm." - what do you see after you enter you login details in "Help | Register."? For me it showed small dialog offering which license to use (for some reason I have 2 in my name one is already expired and one is still valid).
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