You can download a full copy of your entire hosting account, all settings, the website(s), email accounts, and databases as follows:
Log in to your portal as usual: https://my.helpinghost.com/login
Next to the web hosting account to transfer, click on Manage --> Login to cPanel:
Now you are in the cPanel account. Look for the icon called "Backup" and click on it.
Click on Download a Full Account Backup:
Click on generate backup. (1)
You can wait or will receive an email when the backup is complete.
Once it is complete, click on the backup link (2) to download the file to your computer. (This is the file you can give to your new hosting company)