Assume that you have a hybrid deployment of on-premises Microsoft Exchange Server and Exchange Online in Office 365. When you view the cloud-based archive mailbox of a user, archived items are not displayed. Instead, the contents of the cloud-based archive mailbox are the same as the contents of the user's on-premises primary mailbox.
This issue may occur if the user principal name (UPN) of the user's on-premises Exchange mailbox has a suffix that makes it differ from the UPN of the archive mailbox. For example, this issue may occur if the UPN of the user's on-premises mailbox is email@example.com and the UPN of the user's archive mailbox is firstname.lastname@example.org.
This issue may also occur if your on-premises Exchange organization is not federated with Exchange Online correctly.
Make sure that your on-premises Exchange organization is correctly federated with Exchange Online. For more info, see Configure a federation trust.