Google interface allows you to add an external email account to your G Suite. Therefore, you can send and receive emails from your cPanel or Private Email address within Google interface. In order to configure it, follow the steps below:

1. Log in to your G Suite Admin console and go to Apps menu:

2. Choose Google Apps menu:

3. Then choose Gmail > Advanced Settings:

4. Make sure that Allow per-user outbound gateways option is enabled:

And POP and IMAP access option should be disabled:

NOTE: It may take several hours for the system to propagate the changes, wait for at least an hour and then continue configuring your account.

5. Feel free to refer to the following guides to proceed with Google Mail Fetcher setup: