There are many android phone users, to avoid deleting important sms by accident, or just want to read sms on computer, you may need an android file manager to help you to move android sms to computer.

Just google it, you'll find many answers, and I found Coolmuster Android Assistant really helpful. And it's also very easy to use, you just need a few simple steps to move text messages from android phone to pc.

Step 1:Connect Android Phone to PC
Download and install the app on your PC and launch it. The next is connecting your Android phone to PC via usb cable. Then the info of your phone will be shown on an interface.

If this is the first time you connect your android phone to computer, you shoule enable the USB debugging. You can follow the guide to open the USB bugging: Enter "Settings" < Click "Applications" < Click "Development" < Check "USB debugging".

Step 2:Preview messages and Start Export
You can find many icon on the top, find "Contacts" and click it, then go to "SMS", all messages on your android phone will be listed on the right. Then select and check you want to transfer, at last click "Backup" to start the work. And these messages were saved as .txt format on your computer.

That's all!
Resource:
http://www.coolmuster.com/android/view-android-text-messages-on-computer.html