To send using an alias email address in Office 365, the admin will need to create a group and grant necessary permissions to the user. If the user already has an alias address listed as an SMTP address on the mailbox, the address will need to be removed before proceeding with the steps below. To remove the SMTP address, refer to the following article: View, Add, or Remove an Alias (SMTP) Email Address
1. Login to the Office 365 Portal as an administrator.
2. Click the Admin drop down menu on the upper right and select Exchange.
3. On the Exchange Admin Center recipients page, click groups from the top menu, click the Add (+) icon and choose Distribution group to add a new distribution group.
4. In the new distribution group window, add the following information and click save when finished:
5. Double-click the group name.
7. In the pop-up window general section, ensure the Hide this group from address lists is selected.
8. In the delivery management section, select Senders inside and outside of my organization (which will allow users from outside the domain to send email to this address).
9. In the group delegation section, click the Add (+) icon under the send as section to add the alias user, and then click save.
10. Open a new message in Outlook, click on the Options tab and select to show the From field.
11. Click the From pull down, select Other E-mail Address....
12. In the Send From Other E-mail Address pop-up window, type the new alias email address and click OK.
13. The message can now be sent using the new alias email address.