Adding a new domain (company acquisition) to existing Office 365 Environment

When you add the domain, you need to make sure to configure it as Internal Relay in Exchange Online. Otherwise, for any address associated with that domain, Exchange Online will attempt internal delivery, and will fail if no matching account was found. When you set the domain as Internal relay, it will still check for internal matches, but if no such are found it will redirect the message to where the MX record points at currently.