So I searched the web and found jUpgradePro.
Installation and configuration is really easy and starting the migration is as simple as pressing a buton.
I run into some problems, but the support is really fast. Less than 24h I got an answer. My problem is a known bug with restFUL mode and the devs are already fixing it.
So I tried database mode and that worked for me, although I had to manually reorder the menu.
Really great and useful extension.