If the professor doesn't do anything I would schedule a talk with the department head, with all the evidence you've gathered on the lying ham to show how it isn't that the SO is unwilling to work with a group, but that the ham is trying to shirk her duty, and that he tried to seek help from the professor but found none. Maybe the SO can even offer to work alone/start over alone, and let the remaining 3 finish what is left. Give the professor additional options for how to handle the situation that the SO is willing to take. Worst case scenario is that the professor simply has a word with the ham and the ham continues to do nothing, then he is back at square one. Best to nip that in the bud by offering to break off from the group to do his own project, or maybe even he and the normal human agree to split into a group of two/two instead, so at least there is still that "group" aspect to the project.