To do this:
  1. Locate the TeamRaiser Event for which they are a participant
  2. Manage said event
  3. Locate the participant within the event
  4. View their participant profile
  5. Click the link that says "Change Team Membership"
  6. Click the link that says "Make the participant the captain of a new team"
  7. Enter the new Team Name and Goal
  8. Click "Save"

This will effectively transfer them to this new team!