Hello Oscar,
The default Store Manager functionality does not allow to export inventory levels, however this can be done by the custom reports that may be implemented to the application.
Please find more info here:
http://store-manager-for-prestashop-documentation.emagicone.com/prestashop-reports
Also our techs can create a custom report for additional fee. If you're interested, please submit a ticket with the list of the requirements here:
http://support.emagicone.com/submit_ticket