With Outlook, you can receive email sent to one address, and reply to it using another email address. To set this up, you connect all your email accounts to Outlook on the web.
For example, you might receive email sent to your Office 365 email account, but reply to it using your Gmail address.
This article explains how to choose the From email account when you send or reply to an email message.
Send email from a different email address
Sign in to Office 365 and then choose Mail.
Open the message you want to reply to, and then select Reply. (Or create a new email message.)
At the bottom of the message, choose the arrow to list more actions, and then choose Show From.
The From box will appear at the top of the message. Click From. The drop-down menu will list all of the available email addresses for you to reply as.