Apply payment on the back end through Rapid Order Entry.

Go to Attendees or Contacts list and click on the contact name whose invoice you want to make a partial payment on.
In the top right-hand corner of the screen, click the down arrow and select Rapid Order Entry.
Use the search field to look up conference item and select it. You may have to change the Items list to Invoice or Proforma Invoice.
Click Add to Order.
Embed date in names of things in case there are dupes, it helps
May be prompted to enter missing required info
Use optional items to look for items for payment to be added

Sales order report will show source code in order to see discount codes used

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