Hi,
1. Login to cpanel
2. Click Backup
3. Click Download or Generate Full Website backup
4. Next page enter the follwing details
>> Backup Destination : Select Remote FTP Server (Passive Mode Transfer)
>> E-mail id : enter your e-mail id to intimate backup completion
>> Remote Server (FTP/SCP only) : enter ip address of the destination account
>> Remote User (FTP/SCP only) : enter ftp user name
>>Remote Password (FTP/SCP only) : enter ftp password
>> Port (FTP/SCP only) : 21
>> Remote Dir (FTP/SCP only) : /public_html
5. After completing backup it will send a completion mail to your e-mail address
6. Login to your new ftp account and check for the backup.