How to migrate a minecraft server

If you’re migrating from one AMP install to another, you can create a backup on the old system, then create a new instance on the new setup and put that backup in the new instance’s backups folder.
From there you can stop/start the instance and restore the backup, then configure all the MC server’s settings.

If you’re talking about importing a non-AMP MC server into an AMP instance, this guide has the general rundown: