This problem refers to backup purposes. The easiest way to do this is to insert the support CD of your mobile phone into the CD/DVD-Rom and install its original software which is used to back up contacts, sms, install applications, perform maintenance upgrade, recovery, etc.
You should not worry about the connection to the PC since the software provides all the drivers required for this job. After this process completes, connect your phone using the provided cable and from the main interface of the software you perform backup operations regarding SMS messages. It will be presented to you like a wizard which will ask you the format of the text messages, the output folder and additional customization.