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 for the "Be My Love - Large" and a you wish to "Complete" this order in Magento because you will NOT be shipping the customer the remaining items on the order (in this case the "Box Roses with Chocolates"

You click on the "Cancel" button

Click "Ok" (Don't worry this is NOT cancelling the entire will only cancel the items on the order that have NOT been invoiced)

We will now see that the "Box Roses with Chocolates" has been canceled.

The order status has also been changed to "Complete"

In CounterPoint we can now "Cancel" the remaining items on this partial order.

We will notice that there is still Qty of 3 remaining of the "Box Roses with Chocolates" on this order.

Simply click the "Cancel" button

We can see now that the order has been cancelled in CounterPoint