Office 365 supports the use of ‘Send As’ permissions, effectively where Person A appears to send the email, but it has in fact been sent by Person B. This can be particularly useful where Resource Accounts are used and email is sent as, for example, Customer Service, but many people are in fact using that account.

You need to raise a call with the Help Desk (see contact details in footer below) to arrange set-up or for any amendments to 'Send As' permissions of a mailbox.