You can grant the Full Control permission for the Backup Exec service account at the Organization level.
See About granting permissions on the Exchange Server for the Backup Exec service account in the Archiving Option .
To grant permissions at the Organization level for the Backup Exec service account in the Archiving Option
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On the Exchange Server, click Start > All Programs > Microsoft Exchange Server 2007 > Exchange Management Shell.
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Get-OrganizationConfig | Add-ADPermission -User ‘<Domain Name\Backup Exec service account>’ -AccessRights GenericAll -InheritanceType All
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Add-ADPermission -Identity ‘<system mailbox name>’ -User ‘<Domain Name\Backup Exec service account>’ -ExtendedRights ‘Send-as’
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To grant Send As permission on the mailboxes that you created for Backup Exec’s exclusive use, repeat the previous step on the appropriate Exchange Servers.