If you are ever in a position to write a formal letter, criticizing someone for their behavior, and perhaps penalizing them, and the formal letter is likely vetted by your legal people, don't then indulge yourself with gratuitous expressions. Someone may well have proved to be unstable and unreliable, quitting on you in the middle of a semester or project, leaving you with the task of cleaning up after them, and they might well have been manipulative and demanding, but you need not say more than, "We regret your resigning mid-course. And your claims about your colleagues turn out to be not probative. We do hope your find a position more suited to your talents." Get the letter in the mail immediately--for you really do not want them to change their mind.
Never add in something like, "Your behavior is shameful and disgraceful.", even if you believe that as a colleague they have been unprofessional and an embarrassment. There's no need to say more. Wish them well, if need be throw them a big good-bye party. If someone calls for a reference, there are ways of providing something that is bulletproof yet conveys your problem: "While X was assiduous in their paperwork, we do not believe we would employ them again." Say no more.
Keep in mind that their ability to top their past idiocies is very great, so you will find they escalate their outrageous behavior, their accusations against others, their obsessive focus on innocent bystanders, and their assurances that they are right. Don't talk to them if you can possibly avoid it, see them only when others are present, and don't confuse their kindly manner with their being safe and reliable.
