This works for me.

; add admin user to Mailbox Import Export role
New-ManagementRoleAssignment –Role "Mailbox Import Export" –User your_admin_user_name

; trigger the export make sure the target has enough disk space
New-MailboxExportRequest -Mailbox your_mailbox_alias -FilePath \\servername\sharename\path_to_pst\mailbox_alias_mailbox.pst

; check on progress
Get-MailboxExportRequest