You have an Microsoft Exchange hybrid deployment in which cloud-based users in Microsoft Office 365 and on-premises users have the same email namespace (such as firstname.lastname@example.org). However, on-premises users aren't getting email messages from Office 365 users.
Additionally, when an Office 365 user sends an email message to an on-premises user, the Office 365 user receives a nondelivery report (NDR) error message that resembles the following:
#550 5.1.1 RESOLVER.ADR.ExRecipNotFound; not found ##
This occurs if the domain that's set up in the hybrid deployment isn't set as a shared domain in Office 365. To fix this issue, set up the domain as a shared domain. To do this, follow these steps:
lick Admin, and then click Exchange to open the Exchange admin center.
In the left navigation pane of the Exchange admin center, click mail flow, and then click accepted domains.
Double-click the domain that's set up for the hybrid deployment.
Select Shared, and then click save.
The Exchange admin center lists the domains that you added to your account through the Microsoft Office 365 portal. It lets you manage how messages are delivered. In a hybrid scenario, Exchange Online must be set up correctly so that when a cloud-based user sends an email message to an on-premises user, Exchange Online routes the email message to the on-premises messaging environment.
For more info about accepted domains, go to the following Microsoft TechNet website: