Solutions
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FloRyan's post in PMDG 777 + P3D = No Activation? was marked as the answerI got my new license keys but there was no window on the installer to put them in!
I already installed nearly every PMDG airplane on FSX and I know how it should look like on the installer.
For the first time this page with my license info is just completely missing.
Problem solved.
Uninstalled everything from PMDG including Operations Center by hand.
Reinstalled the 777 in P3D and finally, an activation key window!