If your predecessor used the git installation of letsencrypt, you’ll have to run the ./letsencrypt-auto command from the directory to which he cloned the repository.
I’d check the home directory. You might also find some clues if you search his ~/.bash_history file for a git clone line. Alternatively, I suppose you could also just reinstall the client in another directory - I haven’t done that before, but I can’t think of a reason why that wouldn’t work right now.