If you have set up email forwarding in Office 365 to forward emails to your AM account you may receive undeliverable emails from Microsoft if you haven't enabled external forwarding on your Office 365 account. The undeliverable email will look like this:
To stop receiving these bounce back messages you will need to enable external forwarding in your Microsoft account, this setting is turned on by default by Microsoft.
If you are unable to adjust this setting you will need to contact your account administrator, or the reseller (for example Go Daddy), you purchased your Office 365 package from.
Log in to Office 365 at https://security.microsoft.com/ and choose Threat management > Policy > Anti-spam or head directly to the Anti-spam settings page here: https://security.microsoft.com/antispam Note that the policies you see in your own admin may differ from those shown here, as these are only the default policies.
Click on Anti-spam outbound policy (Default) and scroll to click the Edit protection settings link at the bottom of the sidebar.
Find the section called Forwarding Rules, and the dropdown list called Automatic Forwarding Rules. Pull that list down and choose On - Forwarding is enabled. Click Save at the bottom.