Update: Discussion has moved on to a new thread.
After 61 chapters of Harry Potter and the Methods of Rationality and 5 discussion threads with over 500 comments each, HPMOR discussion has graduated from the main page and moved into the Less Wrong discussion section (which seems like a more appropriate location). You can post all of your insights, speculation, and, well, discussion about Eliezer Yudkowsky's Harry Potter fanfic here.
Previous threads are available under the harry_potter tag on the main page (or: one, two, three, four, five); this and future threads will be found under the discussion section tag (since there is a separate tag system for the discussion section). See also the author page for (almost) all things HPMOR, and AdeleneDawner's Author's Notes archive for one thing that the author page is missing.
As a reminder, it's useful to indicate at the start of your comment which chapter you are commenting on. Time passes but your comment stays the same.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically:
You do not need to rot13 anything about HP:MoR or the original Harry Potter series unless you are posting insider information from Eliezer Yudkowsky which is not supposed to be publicly available (which includes public statements by Eliezer that have been retracted).
If there is evidence for X in MOR and/or canon then it's fine to post about X without rot13, even if you also have heard privately from Eliezer that X is true. But you should not post that "Eliezer said X is true" unless you use rot13.
Where on earth would either have gotten the True Cloak of Invisibility? The first note suggests that Santa Claus knows James Potter well and is trusted by him, assuming that the note is telling the truth and Santa did not just steal the cloak from James. That fits Serius or Lupin, or perhaps Pettigrew if he's still alive in MoR.
(Has the guilt/innocence of the Marauders changed from canon? Other things of equal backstory significance have, so I'm uncomfortable just assuming that Pettigrew is guilty.)
Just to reiterate, I really do think it's Sirius! But, devil's advocate.
Slughorn was on good terms with Lily. If he were researching the Deathly Hallows, he'd have an in.
Lockhart may have already been a celebrity. Maybe he wrote a book about going on a quest through darkest New Jersey for the Resurrection Stone, and James was foolish enough to send him the Cloak for analysis. Lockhart is trying to cozy up to Harry anonymously so that, should he end up stealing his identity, there won't be a paper trail.