First, congratulations on your retirement!
The next step depends on how Adagio is currently installed. If Adagio was installed to your computer only (usually the C: drive), then you would need to install Adagio to the server from your successor's computer. In that situation, you would need to request new registration codes (there's no cost).
But if Adagio is already installed to the server, that would make the process simpler. You would only need to run a Workstation installation to your successor's computer (usually no more than 90 seconds).
So the starting point is to understand how Adagio was implemented on your computer. If you want to ease the process, you could get your Adagio consultant involved.