05-29-2013 12:33 PM
Hi and Welcome to the Community!
Per the strict definition of the word "synchronize", I know of no way to accomplish that. But, if we broaden the definition, there may be a possibility.
If you, via the Desktop Software, backup your BB to your PC, you might be able to find a 3rd party PC app that can then parse that proprietary-format file into human readable format for you to then see your SMS messages. This process would of course be considered a "copy" rather than a "synchronize", but if that's what you are looking for, then this should work.
You can find complete backup instructions via the link in my auto-sig on this post. As for parsing the resulting backup file so that you can read it, you can find 3rd party PC apps with just a few minutes searching on Google.