For an existing invoice, open that invoice’s record rather than creating a new one. Share a record-specific editing link, or let the client find the invoice through a Login/Lookup page. Then follow the Stripe payment setup guide to redirect the submitted form to checkout and record the payment status. Opening a form’s general URL depends on its configured access mode; it is not always a create-only flow.
Make sure to watch all these 3 instructional videos in order:
They guide you step-by-step on how to set this up.