Is it wrong for me to email my opponent’s lawyer?

Location: New Jersey

Quick explanation - I run a small business, a client who received my services is now refusing to pay. I contacted our “friend of the family” attorney, who called their lawyer. Their lawyer made an extremely low offer compared to what they actually owe, my lawyer told me about this, and then he became MIA. I’ve emailed him to follow up, and all he said was “please move forward with litigation elsewhere”.

Obviously it’s a low priority, and he doesn’t do litigation, which I will be moving forward with. As of now, the opposing lawyer has no idea that we’re going to next steps. As far as he knows, I’m still considering the low counter offer. Is it wrong for me to send a quick email to their attorney, stating that we will be moving forward with litigation, since my attorney won’t be involved anymore?