Unfortunately, Moves does not provide us with time for all activities. The imported time will be midnight in your selected time zone.
With a Pro Account, you can do a Historic Sync by editing your Moves task and selecting Historic Sync from the toolbar. This will allow you to select the dates you want to copy into FitnessSyncer and the operation will occur in the background. It could take a while to complete and it is recommended that you not change the settings while it is in progress.