Re: Exporting texts/SMSs from "Messages" on iPhone
I used CopyTrans Contacts for Windows (not sure whether it also operates on Mac) to export my iPhone SMS and iMessage text messages to my PC.
Here is where I found out about the tool: How to export iPhone SMS
I do not know the price as I used their free version to export all of my 100+ messages I think you have to pay if you want to export a really large number of SMS text messages.