Exchange administrators do not have rights to log in to user mailboxes by default. Refer to the following article: How do I create an administrator account for login?

Confirm that the admin account has sufficient permissions to log in to user mailboxes:

• Log in to OWA as admin
• Open the end user's mailbox ("open mailbox" action in OWA for Exchange 2007 and later)
• Make sure you can view the Inbox of the end user's mailbox

For Office 365, when you submit a mailbox for migration, MigrationWiz attempts to automatically runs remote PowerShell commands to grant the admin account full permissions on all mailboxes. However, we often see some significant permission replication delays, sometimes exceeding one hour. Therefore, even though the admin account may have been granted sufficient permissions, it may take up to one hour before they become effective. Often your best bet is simply to wait and resubmit for migration.

Note that many hosted service providers will not allow provisioning of a true admin account. Or perhaps you do not have administrative access to the system. In this case, see the following article: How do I migrate if my system does not support administrative credentials?