Custom fulfilment for a collab with another partner

My store is doing a collab with another Shopify partner. We are doing a joint gift box, and are looking for a way to connect the sales. They are managing the shipping so they need to get the orders - but we would love for people to still buy the box on our website.

I have been trying to get more info about custom fulfilment for this 1 product and custom shipping but support still seem to think that this won’t work. If I set up custom fulfilment with our partner’s email, what happens when an order comes in for the gift box? In an ideal world, they would be abler to fulfil the order from their Shopify account with their shipping rates.

Is there an app I could use or does it require a developer? thanks!