I tried this and failed. Not saying it can not be done though. I will tell you what I did.
I have a client that was hosted by a person that offers Cpanel. I offer Plesk. Well this person could not update his site for some odd reason on this host. It would give him blank screens and what not. He called for support but it took days and sometimes weeks for help.
So he contacted me about it. And asked if I could offer him a package for his site. I said sure.
So He gave me his log permission to enter his account and I backed up his site. Took the Tar file and uploaded it to my server. I unpacked it but it was a no go. I had to manually move every folder. I hated it but I am a firm believer in customer service and i told him I could get it moved for him. So I did lol.
I am not sure why it unpacked wrong but i could not get it to work. I am reading my Fedora book to see if it has any answers. But I did get the site moved the long way.
I would love to hear if anyone has a way to do this!!!
If you used command line FTP, you might've transferred the tarfile with the wrong mode. Best you make a .tar.gz and transfer it through binary mode, never had a prob with that this far. At any rate, you can easily copy the site files (public_html) and the MySQL DBs, but the rest might be a prob. Mailboxes and folders might be an easy go (never tried moving them to Plex but mail files work pretty much the same everywhere except M$ Outlook/Exchange), but settings like mailboxes, MySQL users, spamfilters and similar might be difficult to convert if possible at all.