Once you have finished recording a video, your videos will be available in your camera roll.
Make sure Teleprompter has access to your device camera and Photos app. You can check if Teleprompter has access in Settings > Privacy > Camera and Settings > Privacy > Photos.
You will also need to check that your device has enough storage space for your videos. You can manage your storage space on your device in the Settings app, read more information here: https://support.apple.com/en-gb/HT201656