I still don't think it would count as slander. Of course I'm no lawyer but in my opinion the solicitors are instructed by you, you have authorised them to accept service of documents on your behalf. So the letter is sent to them on the basis that you have authorised them to see all communications relating to your divorce. Also your solicitor will not make judgements about your character based on the other sides allegations.
Just out of interest, what did your solicitor have to say about the allegations within the letter?
In my experience, it's better to rise above it unless it impacts on your case. In which case you should disprove the allegations. The other party would have to prove them anyway. Try not to take the comments as personal attacks.
It is a bit odd, because solicitor sent me an email telling me the latest news, but attached was a PDF (This letter lieing about me from his solicitor), I hadn't spotted this PDF at the time. I was printing things off the other day and found it.
So in answer, she didn't say anything about the lie, and I didn't know about it at the time, but I do now!!!!
Sadly I have come to the conclusion from my own situation that you can't win as far as the correspondence goes. I really do feel for you as I know how hurtful it can be but if your STBX is anything like mine and his solicitor I now realise a lot of what they do is to get a reaction from me and I don't let them see that it bothers me anymore.