Maud,
My understanding of your issue is that when the customer is found, but there is no invoice number provided and the payment amount does not match the amount of any open items, the payment is posted on account. But you are expecting an open item to be cleared with the difference posted to the GL account for differences? Without a second match - either on invoice number of on amount, SAP cannot determine which of the open items on the customer should be cleared - so it posts on account.
Say there is a customer with 3 open items (invoices) for $101, $102, and $103, respectively. If I need to post a payment for $100 from this customer, but I have no invoice information, how do I know which of the 3 invoices to clear? This is the same for SAP - if the amounts don't match and there is no invoice number, SAP cannot clear anything and instead posts on account. At that point a user would need to review the on account posting and perhaps follow up with the customer to determine which invoice was paid.
Regards,
Shannon