Allow admin to move customers into organizations

When a user emails the support email address, the user is then added to the customer list for the project. We would like to be able move that user to an organization in the project. Either with drag and drop or a "move" option for the user. The ticket allows for an organization to be added to it, but it does not affect the user. We'd like to be able to move the user so if in the future they log in, they are only seeing tickets for their organization and not all open tickets.