I share this because it was not clear from the tutorial. I used MoveMyMail to transfer a client email to a new server. At first glance it did not appear to have worked. This was because the folders from the old server did not automatically appear. Further investigation using SquirrelMail revealed the folders had been created but it was necessary to "subscribe" to the folders before they could be seen. In the SquirrelMail menu click "Folders" the lower section of the screen will show a list of folders that can be "Subscribed to." Select the folders and subscribe them. Then the folders will appear in the Folder window on the left side of the page.
There you have it; all your email moved to a new server with the existing folder organization. Easy as can be. You just have to know about the subscribe option when dealing with SquirrelMail. Other webmail systems my be similar.
Michael