Within Teamwork Projects, you can move an existing user to a new company.
Note: Only site owners or site admins can edit a users company. Also, a site owner cannot be moved company, they must remain on the owner company.
To make these changes, navigate to the People section of your Teamwork site.
Select the user you wish to move from the list of users. Then to the top right of their details page select the options button (three dots) and then Change Company.
You will then have the option to select a new company to move the user to.
For more information see: Adding or editing a company