The Shopify Private App connection method allows you to retrieve inventory from other Shopify store without the need of installing Stock Sync app on that store.
But the other Shopify store has to create a private app. Steps:
1. Navigate to Shopify Admin > Apps.
2. Click on Manage private apps
3. Click on Create new private app
4. Enter Private app name and emergency developer email.
5. Click on Show inactive Admin API permissions below.
6. Find for Products and change to Read access.
7. Click on Save and Create private app.
8. Copy the API key and Shared Secret.
9. Paste the API key and Secret in respective fields and also the Shopify domain, example.myshopify.com