From the FAQ: Is it possible to apply payment to an invoice ?
Express Accounts uses an account based payment system where payments are applied to the customer's account - not to a specific invoice. This makes it able to handle advance payments or payments without specified invoices much better. When you receive a payment the payment is applied to a customer not a specific invoice. You can however enter a soft cross-reference between a payment and invoice. This is for reference and easy of use only and is optional.
And there is "Payment Ref" column, that is a soft cross-reference between a payment and invoice. But this is just soft reference. Payments are applied to a customer not a spcified invoice