– login to cPanel
– click backups
– click ‘Home Directory’ under Partial Backups
– choose a location on your computer to save the file
– select any/all databases – save those to your computer
– select any/all email filters – save those to your computer
– select any/all email forwards – save those to your computer
– once complete 
– login to cPanel on new host
– click backups
– under Partial Backups
– where ‘Restore a Home Directory Backup’ 
– browse for downloaded home directory
– press upload
– where ‘Restore a MySQL Database’ 
– browse for downloaded databases (ea. must be uploaded individually)
– press upload
– where ‘Restore an Email Forwarders/Filters Backup’ 
– browse for downloaded e-mail files (ea. must be uploaded individually)