Exchange Shell:
Assign Permission – requires logoff/logon before taking effect:
New-ManagementRoleAssignment -Role "Mailbox Import Export" - User "username"
Run Export Request:
New-MailboxExportRequest -Mailbox username -FilePath \\server\share\user.pst
Monitor Status:
Get-MailboxExportRequest | Get-MailboxExportRequestStatistics
Cleanup:
Get-MailboxExportRequest | Remove-MailboxExportRequest
Source: Stevieg