Speak the truth. She is a girl. Going along with a delusion does not cure it but reinforces it. Do not go along with the lies.

Share the truth with everyone, like the Wall Street Journal article by Dr. Paul McHugh.

Discuss WHY she would have this impulse. Is she a tomboy and told that those are signs she’s a boy? Cultivate those interests without the delusion. Does a parent wish they had a boy and are pushing her in this direction both to “have a son” and / or get social activist points?

Is she autistic spectrum? Girls with Aspsbergers are being diagnosed as transgender at several times the rate of anyone else because their mindsets are more toward the mechanical and technical, less social. Not feminine enough in behavior and empathy? Instead of saying tomboy or Aspberger, they say you ARE a boy. And children in that mental frame are susceptible because they don’t know how to argue it and tend to go with the expert unless they ARE the expert in a topic.

Support the normal daughter in this, and back her up when she feels pressured to go along with the delusion. Love on her, let her talk to you. You’ll probably learn a lot of horrifying family dynamics that may be driving this, the same way kids act out when there is a family dispute.