I did the following in the lab to export ALL data from mailbox A to mailbox B.

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1 - You first need to give FullAccess to an Exchange Organization Administrator (in my test I used Administrator) in both Source and Target mailboxes (A and B)

Add-MailboxPermission -Identify A -User “DOMAINNAME\Administrator” -AccessRights FullAccess

Add-MailboxPermission -Identify B -User “DOMAINNAME\Administrator” -AccessRights FullAccess

2 - You then need to export all the data from mailbox A to a folder in mailbox B.

Export-Mailbox -Identity A -TargetFolder “UserAdata” -TargetMailbox B

Note: This last command will export all the data in mailbox A to a folder called “UserAdata” in mailbox B. See below.

You can then remove the FullAccess rights of the Administrator account on both mailboxes (A and B) by launching the Exchange Management Console > Recipient Configuration > Mailbox > right click the desired mailbox and choose Manage Full Access Permission…

You can then delete the Administrator from the list and continue until you finish the wizard.

More info here: http://technet.microsoft.com/en-us/library/bb266964.aspx