If the left transponder is set as the primary transponder, then the normal source of air data is from the left AIMS cabinet. If that data input is lost, the transponder does NOT switch automatically to the alternate source in the right AIMS cabinet, it requires the crew to manually switch via the ALT SOURCE switch on the transponder panel.
The following diagram is from the MAS B777 FCOM. Kindly indicate the "ALT SOURCE" switch.