I originally assumed that a very difficult co-worker was a very inexperienced Junior developer. After talking to the original interviewer, I found out he claimed to have multiple years of experience and was supposed to be a senior developer.
Mystery was solved after I was recommended by LinkedIn to his "second" account: he had certifications showing he actually learned programming basics a few months before being hired, which explains his lack of experience.
He admitted it. Since our company is in an at-will state, he was let go for lying on his resumé; for being difficult to deal with; and for lack of productivity. However, he boasted about going to another company to work as lead developer, and mentioned to some co-workers that he claimed an even bigger amount of development experience to this other company than he did to us.
What is the etiquette here? Should I alert his new company, or just wait if they ask for references? The new company is in the same city as us, but we're unrelated.
EDIT: To answer some questions: Yes I was his direct manager. He did a lot of damage to my team, but nothing personal to me. Btw, we were called by the other company and HR asked me to give references for him. I'm contacting legal about what I should do.