Here via metafandom
.J.K. Rowling has copyright over these characters, and could easily sue.
Except Ms. Rowling has given her blessing to fanfic writers and fanartists. On her personal website, She has featured (and linked to) a site which promotes fanfic/fanart devoted to pairing off Remus Lupin and Sirius Black. She has admitted that Snape/Harry baffles her, but it's more because she can't quite understand why people like Snape so much. As far as explicit content goes, she is all right with it, so long as people don't post it where children can easily get to it.
Now, I have no idea where the picture in question was posted, but I felt the need to point out that not all authors are anti-fanfic/fanart. Some love both, some like one and not the other (Lynn Flewelling, for example, loves fanart but does not permit fanfiction), and some abhor both. I wholeheartedly agree that those authors who don't permit fanart/fanfic should have their wishes respected. But if an author turns a blind eye to it, has openly said he or she permits it, or the work resides in the Public Domain, then I believe the fans aren't doing anything wrong. After all, some of literature's great works are derivatives of other works. My Fair Lady
is a derivative of Shaw's Pygmalion
, which is itself a retelling of a Greek myth. West Side Story
is a derivative of Romeo and Juliet
which is a derivative of Pyramus and Thisbe
Fanfic and fanart take derivative to a different level, but I'm not sure it's as harmful as people make it out to be. The majority of fanfic writers and fan artists love the work and want to be a part of the world that was created. Many do
write their own, original pieces or draw their own art in addition to their fan-related work. As in any group, there are those who take their love of the work to the extreme. And I'd assure you that most fans don't particularly like them either.