How do I bill shipping items on intercompany orders?

I have created shipping items and set up some intercompany orders to test them, but having difficulty understanding the later steps.

After pairing the orders, I managed to add a shipping item to the Sales Order with an amount of $200. I also added shipping items to two item fulfilments of $150 and $300.

When I invoice this, it creates the invoice including the shipping cost of $450 which seems right, overwriting the sales orders and using the costs from the item fulfilments instead. Although frustratingly, the SO doesn't update to $450 and instead still says $200(?)

Thing is, when I go to the Purchase Order, the shipping cost is not reflected on it nor the bill created for it. I have the option to add a shipping item to it, but can't set the cost of it.