The FAA recently approved certification plan, part of a comprehensive process that is an important milestone. The FAA has approved the changes and we will have a series of ground and flight tests and a series of analyses to lead to certifying the airplane.
Boeing is expecting a pretty short testing period for their proposed battery fix though the FAA could mandate more tests.
The presented solution for the 787 battery is a temporary fix that would allow the 787 fleet to get back into the air as soon as possible. But Boeing and its partners should continue developing a permanent fix or a better solution for the Li-Ion battery configuration for coming 777X and other aircraft.
As the root cause is not clear (was it a component issue or was it an integration issue?) it is not clear where the corrective actions should be taken; Japan, UK, France or USA.
Boeing: "We work very hard to design a system that will not fail. Then we assume it will fail and provide redundancies or backups. We apply this design philosophy to every system on the airplane."