If you have our app downloaded, have Mobile Notifications enabled, and have your Agent status currently set to Available, you will receive a push Notification for every new conversation and any conversations you are involved in. You can see more on Notification rules here. You can head to the mobile app or web-based dashboard to respond to the messages.
You will only receive these messages as push notifications and within the Textline app or dashboard - they will not actually forward to your phone's native texting app.
Watch the video tutorial on Setting Notifications here.