Screenshot the conversation to print text messages from iPhone. Open the Messages app and select a conversation. Scroll until the text messages you wish to print are visible on the screen. Press the Sleep/Wake button and Home button simultaneously and let go immediately. Your iPhone screen flashes and takes a screenshot of the displayed messages. Repeat this process until you have screenshots of all the messages you wish to print. But it strips out useful meta information. Maybe you can try FonePaw iOS Transfer, recommended by other post.