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Sales & Customers
I got an option for this in QuickBooks Desktop, shoshifein.
You can create a payment item and add it to the invoice. This will act as a partial payment which reduces the amount due, and this is visible to the invoice form.
- From the Lists menu, choose Item List.
 - Right-click anywhere and select New.
 - In the TYPE drop-down lists, select Payment.
 - Enter the name of the item and select a payment method.
 - Click OK.
 
You can always go back to this thread if you have more questions about handling your customer's payments.