I once taught a rider who was timid and convinced she couldn't do anything right. She wasn't nearly as advanced as your rider, but she had it in her head that she couldn't do "it." In her mind, "it" was anything, whether posting or balancing. I knew she could do a lot of it, but I had to figure out a way to get her to realize it too without stumbling on her lack of confidence.
I put her on a lunge line, and we worked at a walk. Once she was totally comfortable, we started working at a trot. When she was feeling comfortable with that, I had her walk again and asked her to drop her reins, telling her she could hold onto the strap on the saddle if necessary. She did at first, but then she got comfortable and stopped. We the did a trot again, and again I told her she could hold on if she wanted, but she didn't HAVE to. Of course she held on. I gave her a few random instructions during this time, like, "Sitting trot!" or "Stretch into your heels!"... just random things to get her tuned into paying attention to me. Then suddenly I said, "Lift your hands up!" She did it automatically and let go of the strap on the saddle, and about two strides later registered the surprise that she was trotting and not holding onto anything. The look on her face was priceless, and she gained SO much confidence just from that, and after that she had no problems.