I have sql backups copied from server A to server B on a nightly basis.

We want to move the sql server from server A to server B without much downtime, but the files are very large.

I assumed that performing a differential backup and restore would solve the problem with the databases.

1. Copy full backup from server A to copy to server B (10+gb)
2. Open SQL Server Managment Studio on server B
3. Right mouse on databases
4. Restore Database
5. Type in the new DB-name
6. Choose "From Device" and browse to the backup file
7. Click Okay. This is now resorting the original "full" backup.
8. Test new db with dev application - everything works :)
9. On original database rightmouse on DB > Tasks > Backup...
10. Backup Type = Differential, Backup to disk, add a new file, and remove the old one (it needs to be a small file to transfer for the smallest amount of outage)
11. Copy the diff backup onto the new db
12. Right mouse on DB > Tasks > Restore > Database

This is where I get stuck. If I add both the new differential file, and the original backup to the restore process I get an error

The media loaded on "M:\path\to\backup\full.bak" is formatted to support 1 media families, but 2 media families are expected according to the backup device specification.
RESTORE HEADERONLY is terminating abnormally.

But if I try to restore using just the differential file I get

System.Data.SqlClient.SqlError: The log or differential backup cannot be restored because no files are ready to rollforward. (Microsoft.SqlServer.Smo)

Any idea how to do it? Is there a better way of restoring backups with limited downtime?