An update has been deployed to Office 365 which allow you to get your invoice being sent by email.
To enable this, just logon to your Office 365 administration portal and reach the Billing notifications section
Then Turn on the functionality
The next invoice will be automatically sent to all your Global Administrator and Billing accounts.
As the recipients list is being displayed below the toggle, you can also review it and adjust.
Can not wait to get the same for Azure and the ability to select to who to sent it; it could be better to be able to send it to a DL which may be tight with an automated invoice management system.