Connect your phone to PC using the data cable and Motorola Phone Tools.
Then when you get the main window with your phone pic and panel leave your phone idle for some time. After some time you can see a flashing envelop. Click on it. It will take you to your inbox. From there double click on each sms and then copy the whole text of the sms and paste it in a word file.
And you are done. See if it works. At least it works for me.