In this guide, I am going to walk you through turning on the "From" field to send an email from a different account you have permission to send mail on behalf of.
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 the drop-down list, right next to the Send button, click on "From", 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.