At times, you may want to have another user receive a copy of a user’s inbound emails, such as if a user goes on holiday or leaves the organisation. Applying mailbox forwarding allows the copy of those emails to be automatically forwarded to another user when they are received by Office 365.
NOTE: It is possible to forward to external email addresses, however if they apply DMARC checks to inbound emails, commonly used by free-mail domains such as outlook.com or gmail.com, these may get picked up as spam or blocked by that recipient.
You will need to have the Exchange Admin role or greater to make these changes.
Apply Mailbox Forwarding
Forwarding applied this way will be visible to the user in their Outlook on the Web settings. It is also possible for a user to set their own forwarding within the Outlook on the Web application.