Processing a partial order fulfillment with a verified payment

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We have setup the both order processing and payment processing to manual requires Associate to process the invoice
If we are able to fulfill part of the order with a verified shopify payment ( not processed yet ). 

Do we need to void the entire order and either have the customer or an associate refill the order with items available to generate a new invoice with a verified payment ( not processed ).


Is it as simple as making the adjustment on the invoice during the fulfillment, send the correction and process the verified payment for the items purchased, which could be less or more than the verified shopify payment amount?

The topics online does not really explain this situation..