Oh my gosh this is perfection. Please write a sequel. It could be like the second episode where they finally catch Maggie. Your win was well, well deserved.
Chapter 2 and 3 were also amazing!! I really like where you're going with this and the character Annie is becoming. She is so clever and I really like her! I can't wait to see what happens next!!
Literally, the only thing I found wrong with this piece was in this line, "A piece for fabric was clenched between his teeth" I think you meant of instead of for. Other than that, you did amazing!
J.J. explaining the case to the team was just perfect. It felt so much like what would occur in the show, and I think you did a really good job with it. It just mirrored the show so well and I loved it!!
I think your flashbacks were brilliant. You started with a description of the pain the Reid was in, and a small glimpse at what had happened to him, and then related it back to the case that had led him there. It was really well executed!
Rossi was just cracking me up in the beginning, "What the Hell kind of books are you reading?” That is totally something he would say. It matched his character so well and made me laugh, so big bonus points there!
I love the way Reid picked up on all the visual clues about the girl, and that you related them back to the reader. You didn't just say the strange things about her, but you also explained the detail of her looks, from Reid's point of view, and you did it in a way that made me feel as thought that was how he felt she looked, and it wasn't just a plain description of her.
I really can't wait to see where else you go with this and how it ends! You left it on a cliffhanger, but it was a good one! I can't wait until you update again!
Random Thoughts: "legs felt like they were made of jelly." Using jelly to describe something as wobbly would have been a phrase I thought was popular, but I've never seen it done before, especially not on this site. And I think it was a really neat way to relate the feeling back to readers.