The tool says that both servers need the same OS and configuration. Okay, to what end? I assume this means Ubuntu & Ubuntu or CentOS & CentOS. Not Ubuntu 14.04 LTS to Ubuntu 18.04 LTS. It also calls for the same configuration, okay, to what end? Can't have the same IP's, and the mere fact the target server is newer and different hardware will by definition mean it's got a different configuration. I don't want to assume as you know what happens when one assumes in IT.
It does not. Migration tool works with disparate end points. You are confusing Migration Tool with ISPCopy from the same toolkit.
Is it possible to use the migration tool to migrate a single website from an old ISPconfig server to a new one?
