I recently passed my master's examination which is equivalent to defending a thesis. Should I notify law schools of this?
Passing your master's exam is a big step towards completing your master's degree, so congratulations on that. And yes, you should update your applications with that news. Any meaningful change in your educational credentials or profile constitutes a legitimate update.
In your update, explain what steps your master's degree requires, because not everyone will know that "passing a master's examination" is the same thing at your program as "defending a thesis" is elsewhere. That way, you can put your master's examination in context and give admissions officers a better sense of how close you are to the finish line. You probably won't be surprised to hear that a number of applicants start master's programs at some point but never get around to finishing them. The fact that you're on track to finish yours will be a good update for them to hear.
And if you haven't already done so, take this update opportunity to educate them about the nature of your master's program. In terms of caliber, there is such a wide variety of master's programs out there that it can be hard for admissions officers to know how rigorous they are unless you tell them. You won't need to take this step if you're in a well known master's program (e.g. MPP from the Kennedy School), but most master's degrees are not going to be all that familiar to law school admissions officers.
This is also a good time for me to remind applicants more generally that if they are still stuck in limbo — meaning, they haven't yet received a final decision on their application — they should not bombard admissions officers with gratuitous updates, because updates need to rise to a certain level of importance to merit an admissions officer's time. For example, it would not be a good use of her time to read updates about this 5-page paper or that 10-page paper that someone wrote for a class. As always, exercise some discretion about what information you send in to update your file.
Here's a test: if the subject of your update is something that would have merited a bullet point on your resume when you first submitted your application, then it counts as a meaningful update after you've submitted. If it wouldn't have merited space on your resume (or in your application more generally) back then, then it would not be an update you should send later in the application cycle either. In this case, passing your master's examination would be a good bullet to have on your resume, so that news is a legitimate update to your file. You can give schools that update via email.
More advice on updating your applications: Updating Your Submitted Law School Applications.
Former Dean of Admissions at the University of Chicago Law School and a recovering lawyer, Anna Ivey founded Ivey Consulting to help college, law school, and MBA applicants navigate the admissions process. Read more admissions tips in The Ivey Guide to Law School Admissions, recently updated and available as an e-book. Follow Anna on Twitter (@annaivey).