Cal here from Shopify, thanks for reaching out to us!
While you can't integrate those orders directly into the 'Orders' section of your admin, you can set yourself up as 'third party fulfilment', and then add them as draft orders later. Operating as a fulfilment service would mean that you receive an email from the other business automatically every time they receive an order for those products. Within the email, you would receive data like the customer shipping information, the products ordered etc, which you can use to create your draft order in your own admin.
You can read how to add yourself as a fulfilment service to that first store here. Then the other store would simply add you as the vendor and add you in the 'fulfilled by' sections for the relevant products so you receive those fulfilment emails.
Let me know how it goes, I suggest testing it out on a sample product first and placing some test orders to get used to the flow!