At what point is the FAA required to relinquish control of the investigation process to the NTSB?
a simple sentence answer to a simple sentence question.
"anytime they are asked"
Fundamentally the FAA is a regulator and seeks information in order to act against it's regulations.
The NTSB is an investigator and seeks answers to causal chains and weighing of contributing factors. They also look for holes in regulations as well as unregulated procedures.
Together they do a pretty good job. In many cases the FAA action is taken even before an investigation is finished.