I have seen this case from a forum where an iPhone user asks to print text messages from iPhone. There are two common ways to keep text messages to help this questioner. One is to take screen-shot to save the iMessage records, but it is not so reasonable since you need to view the messages in photos one by one.
On the other hand, downloading text messages as HTML/CSV/TXT format is practical to save them as evidence and convenient to read. In this case, iOS Transfer, which is contributed to transferring data among iOS devices, including iPhone 6/6 Plus/5s/5, offers help to print text messages for the questioner to work out his problem.
With this software, you're allowed to print out text messages/MMS/iMessages with attachment. Follow it to learn how to download your iPhone SMS.
At first, connect your iPhone to computer after installing iOS Transfer on PC. Then, you'll be asked to select "Trust" on your iPhone.
Step 2 Choose SMS to Export
There are six kinds of data on the left sidebar, so select "SMS" to gain your iPhone text messages. When you gain the following interface with numerous messages, select what you tend to export and click "Export to" > "Export Selected Messages" to choose one of the three files. Here HTML format is suggested because it is clear to read and convenient to print out.
Notes: You can also choose "Export All Messages" to download but it is necessary to tick the box in front of the record. Otherwise, the options on the top would not be clicked.
Another approach can be dealt with this issue. After selecting certain messages on the contents, right-click the chosen one to press "Export Selected Messages" and choose HTML/CSV/TXT file to print.
Notes: In this way, if you select "Check All/Uncheck All" to view the SMS on the right.
Step 3 Print Text Messages with Printer
After waiting for a few minutes, the text messages could be outputed as a file on your computer, but you are required to connect your PC to a printer to print it out.
Notes: HTML format allows you to view your messages conversation clearly and if you tend to export some images in the conversation, it also works.
What a easy way it is to print text messages from iPhone! Such a powerful program does not only work for messages managing, but also serves for saving other data shown on the left on the screenshots above.