How to get my text messages off of my iPhone 4s onto my iPhone 5s?

I just bought an iPhone 5s after the Wi-Fi on my 4s stopped working a few days ago. My new phone backed up all of the text messages I had from before I lost Wi-Fi, but it did not back up the ones after I lost Wi-Fi. I need to get the messages from the last few days I had my 4s onto my new phone but I'm not sure how to do that. Is there any way to get the messages on my 4s to my 5s without having Wi-Fi or 3G on my 4s?

Usually a backup of the old iPhone & then a restore from that backup on the new would do this. Using iTunes of course to do it.

You may try this Phone transfer. I know it can transfer the messages between your iPhone 4s and iPhone 5s. It worked fairly well for me.