Can you upload text messages from an iphone 5 to your computer?

I have an iPhone 5, and I want to log a bunch of my text messages from some people, mainly because the whole long text string is entertaining and I wanted to share it with friends/the internet. How do I go about doing that? I don't want to take a bunch of screenshots, because that would take forever.

Yes… Take a bunch of screen shots of the chat (LOL) plug your iphone in. Look for the pictures. Drag them into a folder. And do whatever you want with it