H4 to H1 COS with approved H1B petition

I have an approved H1B petition in India from Employer A filed in 2012, which is not stamped. In the meantime, i travelled to US on H4 in 2013. Can other Employer B now file a COS from H4 to H1 by filing a new petition under cap-exempt providing the approved petition details or do i need only Employer A to file COS.

New employer can file H1B transfer under cap-exempt.