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Sounds like your integration is trying to add a line to pay the invoice rather than selecting the existing line. You usually have to match the payment to the invoice using the internal or external id.

Then you're selecting an internal id that isn't on the apply payment sublist. The apply list is only going to show invoices that match the customer, subsidiary, and AR account used on the payment. Also, trying to apply to a paid invoice throws the same kind of error.