Yes it is.
Who is hosting your Filemaker File? What you do is take a copy of your filemaker file from the old Filemaker server, and upload it to the new Filemaker server.
If there are server schedules setup, e.g. a script run nightly then they will need to be re-setup. Also if your database is encrypted the new server will need to know the encryption password.
Also the new filemaker server will need to have purchased webdirect client licences as per the filemaker licensing fees.
Externally stored containers must be moved manually.