I appreciate you for getting back to us here in the Community. Allow me to chime in and help provide information about your Customer Statement concern in QuickBooks Desktop.
For now, the only option available is the report shared by my colleague above. Right now, customizing customer statements to show invoices and its payments are unavailable.
I'm personally taking note of your request regarding the customer payments in QuickBooks Desktop. It would also be best making sure you always have the latest release to ensure any new features from the product engineers will be on your program.
For additional insights on the steps, I'm adding the article I recommend on this:
Please feel free to post any questions you have below regarding the customer statements. The Community will be here to help.