can i save text history from my iphone to my computer?

The only thing that happens when you sync regarding SMS is that it is saved in the backup file. There are 3rd party softwares out there that are able to get into the backup file, and there is also software out there you can put on the computer and extract the SMS from the phone (Touch Copy). Up to you which way you want to do it.

Touch Copy is one I use, and for something that is for backup extraction I think it is called Backup Extractor.

They are not in the App store. They are not applications but 3rd party software for your computer to extract that information. Sorry, I must not have explained that good enough.

You're welcome.

Yes, your text history does get synced to your computer, if you sync it with a Mac. I have changed phones and re-sync to new phone and was able to get ALL my text history back. I have texts dated back to 2008! Lol :)

I called tech support and they showed me how to retrieve specific dated syncs.