I still don't see the argument, because I don't see where writing the letter translates to
me claiming anything. Like, imagine that I wrote the letter as a text that would appear in a novel. And then someone else, reading my book, copy-and-pasted that text into an email and sent it to someone. I'm quite certain I'm not claiming to be a lawyer at
that point (although the person who copied the text might now be, I guess.) What is the smallest change you can make to what I did by writing the novel, that would push it over the line into being a criminal act? When does a text change from fiction into a claim about reality?
I don't think the "walking up to someone" analogy applies, because there's a "me" doing that walking that the person can see, and so by asserting any claim through speech, I'd be attaching the subject of that claim to the person they're seeing—i.e. to myself. But in sending a letter written "as" someone else, there is no "me" from their perspective to attach the claim to. There's only "whoever is named [fake lawyer name]" (nobody) and "whoever sent this letter" (someone else, although I paid them to do it. Coincidentally, if I did have a lawyer, I'd be paying them to do it.)