Is there any reason you wouldn't want to simply use a full backup of the account itself instead and generate it using cPanel > Backups > Download or Generate a Full Backup area?
After you have the backup file, you could just ask the provider of the new server to restore it, which would restore everything for that account. Since you are moving the account to their machine, they should be happy to restore it for you. Even if the account already exists on the new machine, you could ask them to do a forced restore:
Where username is the cPanel username.
/scripts/restorepkg --force username