Forwarding emails out of your domain lately has been stubbed by many large providers such as Microsoft, Google, and Yahoo. This has to do with the new requirements around SPF using DKIM and DMARC records. Currently, if you attempt to setup a forwarder on your domain to one of these providers, depending on the configuration of the upstream sender, it may end in an error such as:
550 5.7.1 Unauthenticated email from email bedbathandbeyond.com is not accepted due to domain's DMARC policy. Please contact the administrator of bedbathandbeyond.com domain if this was a legitimate mail. Please visit https://support.google.com/mail/answer/2451690 to learn about the DMARC initiative. i24si39961717edg.100 - gsmtp
To work around this issue, we recommend creating a normal mailbox for your forwarder on our system, then use the remote mail service to log into it and gather the emails.
Additional information specific to Google on how to do this can be found here:
Additional information specific to Microsoft Outlook.com can be found here: