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In this guide I am going to walk you through turning on the "From" filed to send an email from a different account you have permission to send mail on behalf of it.
Step 1: In O365 click on New mail
Step 2: Click on Options, then click on the check box for Show From
Step 3: From will show right next to the Send button, click on it and you will get a list of accounts you have permission to send from. If you do not see it listed, click on Other email addresses...
From the search, type in the email account you have permission to send mail from. You should now be sending an email via that account.