One of the really nice things that you can do with Office 365 Exchange Online is configure your Exchange Online mailbox to receive from your other external email accounts.
To do this first login into your Office 365 console via https://login.microsoftonline.com. Then select Outlook. You should then see your mail box.
Go to the top right of the window and select Options (which is just under the user name).
From the menu that appears select See All Options. You should then see a screen like:
You should be on the Account option. To the right you’ll see the Connected Accounts button, select this.
Select the New button.
Enter an email address and password, then press the Next button.
After a few moments the account should show as being connected (if additional information is not required).
When you are returned to the Connected Accounts screen you should see your account listed. You’ll also note on the right the option to change the Default Reply Option.
Mail from the connected account will now start appearing in your Office 365 Exchange Online email box (as well as in the original external mailbox).