Transferring Temporary Resident Permit

My son's work contract ends in January 2015 but his Temporary Resident Permit (TRP) will expire in April 2015.
He has to renew his US passport in February 2015 and plans to get another job in China. My question is
does he need to transfer his (TRP) from his old passport to his new passport before his TRP expires in April 2015
or leave it to the new employer to get him a new TRP, leaving the present TRP in the old passport.
Will he get fined if he does not do it soon because it will take some time to get the documents approved for the new job. Can his present employer helps him transfer the TRP expiring in April 2015 to the new passport after the contract ends in January 2015