Note: This process works only when the payment method has been configured to "Authorize Only" when the order is placed. If the payment was "Authorized and Captured" a credit memo will need to be issued.
When an order has been partially invoiced and partially shipped as seen here and you want to "Complete" this order in Magento because you will NOT be shipping the customer the remaining items on the order
You click on the "Cancel" button
Click "Ok" (Don't worry this is NOT cancelling the entire order...it will only cancel the items on the order that have NOT been invoiced)
We will now see that the line item that was NOT invoiced/shipped has been canceled.
The order status has also been changed to "Complete"