Yes. When an inbound text arrives, Sprwt saves it and — as long as notifications are turned on — immediately creates an "SMS received" bell notification. If that number has Redirect SMS? turned on, Sprwt also queues a copy of the message as an outbound text; in the current version there's no separate field for a distinct forwarding destination (only a Yes/No toggle), so exactly where a "redirected" message ends up isn't fully clear from the setup screen alone — treat that specific detail as unconfirmed if you're relying on it.