Great question — answering as the UphillTech team:
One possibility would be to expose a web service interface on your inventory management system that allows the transactions used by the web shopfront to be accessed remotely. With a reasonably secure VPN link or ssh tunnel type arrangement, the web shopfront could get stock levels, place orders or execute searches against the inventory system. Notes: You would still have to add a reasonable security layer to the inventory service in case the web shopfront was compromised. You would have to make sure your inventory management application and server was big enough to handle the load, or could be reasonably easily scaled so it could do so. Your SLA for the inventory application would need to...
Full answer by ConcernedOfTunbridgeWells: https://stackoverflow.stackexchange.com/a/487660 (CC BY-SA 4.0).
Need it done for your business? UphillTech.