Hi
You would still need access to export them. your batch file would need to be run to include powershell snap-ins etc.
The best would be to grant you the relevant rights to export mailboxes to pst.
Seems like, this informative article would be a good approach to resolve your concern : http://www.msexchange.org/articles-tutorials/exchange-server-2013/management-administration/managing-pst-import-export-process-exchange-server-2013-part2.html
Moreover if you wish, you may also give a shot to this automated solution (http://www.exchangemailboxtopst.org/) in order to accomplish this job in more easier and quicker way.
Seems like, this informative article would be a good approach to resolve your concern : http://www.msexchange.org/articles-tutorials/exchange-server-2013/management-administration/managing-pst-import-export-process-exchange-server-2013-part2.html
Moreover if you wish, you may also give a shot to this automated solution (http://www.exchangemailboxtopst.org/) in order to accomplish this job in more easier and quicker way.
- Proposed as answer by Allen_WangJFMicrosoft contingent staff, Moderator 2 minutes ago
This might work for you http://www.intelliadmin.com/index.php/2011/04/backup-outlook-from-the-command-line/