We totally get it - productions are always better with a crew. Here's what you can do to help fix this.
If you've recently added a friend on Facebook, you'll need to close and relaunch your game. Once you're back, your new friend should be waiting for you in the cast list of players you can send a Card to.
If you've restarted your game and you still can't see your friend, there might be something else going on. Check out this Help Center article for other possible solutions.
Enjoy building your studio with your friends!