There's an app call Power Sync that transfers Apple Watch data to Fitbit, however it is my understanding is that the data synced via Power Sync cannot be used for challenges. I suggest doing some research on the Power Sync app.
Now that I read more carefully about Power Sync ([URL="https://itunes.apple.com/us/app/power-sync-for-fitbit-sync-to-health-app/id1071544839?mt=8&at=10l3Vy]link[/URL]), it appears to send Fitbit data to the Health app, not the other way around.
Sync Solver ([URL="https://itunes.apple.com/us/app/sync-solver-for-fitbit/id935306292?mt=8&at=10l3Vy]link[/URL]) may be the only program that puts Health data on Fitbit.
Try this app - [URL="https://itunes.apple.com/us/app/myfitnesssync-for-fitbit-apple-health-to-fitbit/id1240275160?mt=8&at=10l3Vy]myFitnessSync - Apple Health to Fitbit[/URL] It worked for me. Transfers my Steps from my Apple Watch and my Weight from Withings scale to my Fitbit account.
Your steps won't count towards weekly challenges. Fitbit only allows steps from a Fitbit or your phone to compete in challenges.