A student needs to be enrolled (associated) with an organization for testing. You can transfer student's enrollment from one organization to another through request and approval process as explained on this and 3.1 NEW Authorization for Enrollment Transfer page.
To send a transfer request, follow these steps:
From Setup > Work Requests, click the Work Type filter and select Enrollment Transfer. Select an enrollment request(s).
Click the Select Tasks drop-down and select Request / Edit Final Reporting. Click Start.
Select the transfer request, and click Send Request.
To understand the approval process, see 3.1 NEW Authorization for Enrollment Transfer.