Yes! Each fortune is a unique ERC20 token! Not only can you send it, you can trade it, sell it, and if it’s listed on an exchange you can day trade it! Partial tokens can’t be sent. This is meant to keep the fortune and the token attached forever. There are ways to pick and choose which specific token/fortune you’d like to send to a friend.
One more thing, if you give it to a friend, the newer wallets auto detect tokens and it should magically appear in your friends wallet with the fortune on display!