Transfers board ownership between different teams/accounts

Hi all,

Hoping someone can help with this. I need to transfer a board from one team (company A) to another team (company B). Looking for ideas on most efficient way to do this.  They are two different companies with two different Trello accounts.  At the moment the company that owns the board (company A) has given access to the other company (company B), but now company B wants to take over the board and give access to company A (essentially switching roles).  Company A should have should have access to be able to still add cards to the board.

Appreciate your comments.

Thanks!