I have a credit note from the prior year that has been applied to an invoice. However, the income statement only shows the income from the invoice, not the nett zero amount after application of the CR.
That sounds about right. The invoice you issued now should appear on your income statement. The overpayment you received last year was probably in your accounts payable on the balance sheet. Now that you’ve used the credit note the amount in accounts payable would have been zeroed out. Instead of receiving the money from the invoice in your bank account now, you have reduced a debt instead.
The credit from the credit note will show up on the income statement based on the date of the credit note, not the date of the invoice that was credited.
If you want to effect the previous year’s P & L, then you should use an accrual journal entry to debit the income account and credit the accrual liability account dated ghe closing date.