Sometime accounts are to big to transfer via the WHM transfer feature.
Below you can find some steps to do so manually
Log into your server and create a cPanel backup for the account
<username> refers to the username you want to backup.
/home is the path to where the backup will be placed.
After the backup has been completed you can simple move it by pushing it via SCP
here is the tutorial http://wiredgorilla.com.au/moving-large-files-linux-server-linux-server/