回复：Updating DS-2019 of J-1 does not hurt his status - 回复：Correct

I do not find a lot of information about that if the J1 program transfer, whether the J2 EAD is still valid.

Here is the some infromation I copied from:
http://www.columbia.edu/cu/isso/visa/scholar/J-2_employment_authorization.html

If the J-1 visitor discontinues the program at Columbia or changes to another visa category, the work authorization for the J-2 dependent will be withdrawn. Legal work authorization for J-2 dependents is always dependent on the status of the J-1 principal.