For a packer to be able to Add Stock to an Order at the Packing / Packed the stock item must be linked to the customer. It is possible to add a Stock Link at the Pending Order stage but not when it moves to Packing / Packed.
The other option is to make an item a COG item (Stock Category) and then you can add any COG item to any Order, noting that it will use the Master Stock Price for the COG item. If you want to use a Customer Stock Price you will need to link the Stock Item to the Customer.