It's really easy to recover iPhone text messages to Mac if you get in the right way. Although you can use iTunes to backup your iPhone text messages, but iTunes backup all the text messages in one single file, you cannot view them one-by-one. If you just want to recover/transfer certain messages to your Mac, this step by step guide will help you a lot.
This guide supports all series of iPhone including the latest iPhone 6S & iPhone 6S Plus. What you need is this iPhone Data Recovery. It's available on both Mac and Windows. And I will take the Mac version as sample in this guide.
Step 1. Download the iPhone Data Recovery, double click the setup file to install it, and then launch it. Connect your iPhone to Mac with the USB cable. The program will detect your iPhone in a few seconds as follow screen.
Step 2. Click the "Start" button, and the program will scan all the text messages on your iPhone. It will takes you a few minutes to finish the process depends on your iPhone data size. Besides, during the process, you can see other data on your iPhone be sorted into category as well.
Step 3. When the scan progress is finished, click "Messages" in the left sidebar, and you will see all the text messages on your iPhone, including the deleted text messages. Just check the messages that you want to copy from iPhone to Mac and click the "Recover" button. In the pop-up, choose "Recover to Computer", the program will start to copy iPhone messages automatically. You can also recover text messages attachments from iPhone to Mac by clicking 'Message Attachments' in the left bar and checking the wanted attachments.