When the Exchange Migrator runs it checks to see if the Admin account specified has access to the mailbox it is operating against. If it does not, it assigns itself permission and then waits 15 minutes for the permissions to take effect. To prevent this delay you must grant your admin account full access to your Office 365 mailboxes before running the Migrator. To do that you must first connect to the remote PowerShell in Office 365.
After you are connected, run the following command to give your admin account full access to all mailboxes:
Get-Mailbox -resultsize unlimited| Add-mailboxpermission -user [email protected] -AccessRights FullAccess -Automapping $false
Or run this command to give the account access to a single mailbox:
To later remove the permissions, run the following command:
Get-Mailbox -resultsize unlimited| Remove-mailboxpermission -user [email protected] -AccessRights FullAccess
Updated: April 16, 2016