You cannot forward Moodle email to another email address. You can, however, receive an email alert that you have Moodle email.
To receive Moodle email alerts:
In your Moodle course, under the eMail list block
Click Settings (top right corner)
Do you wish to receive alerts for new messages? Yes
Click Save changes
You only have to do this once and email alerts for all your Moodle courses will be sent to your BCC student email account.
The alert will tell you which Moodle course you have the email in.
You will have to login to the Moodle course and click Inbox to read the email.