There have been quite a few solutions over the years that allow you to backup your BlackBerry SMS but Txt2mbox seems to do it a bit differently over IMAP. What it does is backup your sent and received SMS text messages to your webmail email as long as you have IMAP access to your account. If you have Gmail and other good email services then this works like a charm. If you have an email account like Hotmail or Yahoo you will need their premium paid email to get IMAP access.
Either way Txt2mbox works by using IMAP to access your email and putting your sent SMS in your sent mail folder and putting your received email in your inbox. The app also nicely has a free trial in App World after which you can pick it up for $2.99 or you can find more info on their website.