I was really hoping this one was true, just because it would have been so interesting. But alas, I found nothing. I searched all the psychology databases I have access to and nothing. Zip. Nada.
Google gave me a bunch of shady blogs with the same quote but no source. One result did give me something different, though. An article on The Marietta Times sourced Ken Yenke (a toy and doll expert) as saying that “The natural product of wool (mohair), of which many teddy bears are made, helps release endorphins in humans which produces a comforting, relaxation effect, according to a recent scientific study.”
Again, I searched Wool and Endorphins and found nothing that looked remotely reliable. I did, however, find a magazine site where people ask Ken Yenke various questions about their teddy bears. In one of the entries, Yenke tells a person that “100% wool helps you sleep 30% better by releasing endorphins!” But again, no source.
I think it’s safe to say whoever made this meme (wasn’t me, I swear!) will be disappointed: