Moving a board to a different team
You can change the team that a board belongs to by opening the right sidebar on the board, selecting "More", then "Settings", and "Change Team." Select the team you would like your board to belong to from the drop down menu.
You have to be an admin of the board to change its team.
You can also change the team that a board is associated with by clicking the team's name in your board's header to the right of your board's name, selecting "Change Team" and then choosing the team you would like to now associate your board with.