Hey @YuriiTyvodar ,
I actually do a lot of work in this area. I’d tackle this using Shopify’s webhooks + the API. Effectively the way it would work is whenever a product’s inventory level is updated on Shopify (via a transaction etc) you’d receive a message into your other system saying update this inventory level to X. You’ll also do it the other way, when the other store updates the inventory for an item, you’d feed it through to Shopify and update the inventory level there.
Let me know if this is something you’d like help with, I’m a Shopify Partner and do a lot of work with APIs and integrations.
Thanks,
Matt