Hi and welcome,
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Yes, you can just activate your Full version. That’s it. You don’t have to reinstall it. It’s the very same installer and executable, as the Trial.
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First you have to activate the license to the Soft-eLicenser. Then you can immediately transfer it to the USB-eLicense. Be aware, you cannot transfer it from the USB-eLicenser back to the Soft-eLicenser.