Dave,
If you have your account set up with LMFS, then when you File a plan, those are available for fiewing on the website. However, it does not automatically show your briefing that you viewed on the device. You have an option on the website that alllows for a Briefing for that flight. I just tested this, Filed, Viewed Briefing, then went to the website, and it showed the Proposed Flight, but there was no briefing listed. There was an option in the Action drop down to get a Standard Briefing.
I'll bring this up as it would be nice to sync that briefing. Also, I noticed a bug. If I File on the device, then cancel on the LMFS site, the device will still show as filed and not let you cancel. It pops an error, that it could not be cancelled, with an option to treat as open or cancelled. I'm reporting the as a possible bug. I think it should check the status on the LMFS site and update that on the device or at least prompt to confirm the correct state of the flight plan.