Hello Matt,
Studio 3.8 server is compatible with both Windows Server 2008 R2, and Server 2012.
The migration procedure is to first install 3.8 on your new server, then move your application over to the new server and to launch Network Configuration>Start New Monitor and associate the port with your application. As for licensing you should be able to use the licenses from previous version.
We have seen a number of cases when updating that applications require additional Windows permissions which require you to run the studio server as a desktop application and not as the default service. To configure this you would first need to stop and disable the WavelinkServer and WavelinkStartupSrvc services. Once disabled launch start>Wavelink Studio>Wavelink Studio Server. This will start the server with additional permissions. To then have this always startup as a desktop service you would need to copy the Wavelink Studio Server shortcut into the appropriate startup folder, and have a user login each reboot.
Please let me know if you have any additional questions about this.
Thanks,
Nick