It seems like all other fitness services (like Endomondo, Runkepper, Garmin etc.) supports synchronization to other such service. But Fitbit does not support this, unfortunately and surprisingly.
Fitbit only syncs Steps, Distance, and Sleep. Consequently, Fitbit does not sync exercises/runs, distance and time, heart rate, gps data (if recorded with the Fitbit app), etc. to Endomondo.
Fitbit should really consider to support synchronization of all data from Fitbit -> Endomondo (and other similar services). It seems like your users want to keep using services like Endomondo, Runkeeper etc. but would like to use Fitbit's hardware. As it is now, this is not possible.
Moderator Edit: Added Labels
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