... Hold on, are you just now realising that fraud isn't legal? Like, it's one of the first things to have been illegal; the oldest legal codes that we know about cover it.

That said this isn't a criminal case and the state isn't prosecuting anyone. (Yet; I assume the person might be prosecuted at some point)

And this is fraud... how? Because a guy made up fake stories and gave them to a newspaper for free? Or because he posted untrue things on Twitter? I guess the folks at The Onion better expect police knocking at their door any day now. They make up documents and quotes from "government officials" all the time. Better arrest them!

Who else would prosecute people for spreading fake documents? Do you think a civil suit would be more effective?

In this case it's a civil lawsuit, and the Twitter user isn't being charged with anything.

Not yet

The state isn't prosecuting anyone. It's a civil lawsuit.