Hi, I'm Arlene, an independent advisor — thanks for reaching out
Only the organizer (your mother) can remove your son's account from her family group. She needs to go to family.microsoft.com, sign in, select your son's name, and click "Remove from family group." After that, you can add him to your own group. There's no other way to move a child account Microsoft requires the organizer to remove it first.
Hope it helps. Please let me know if you need further assistance.
Regards,
Arlene D.