A possible solution for the problem you are talking about is Distributed File System – DFS.
I would install one DFS root at the main office and at least a second in the branch office F.
With DFS you can replicate a folder on more usually multiple folders across the same or multiple sites. This way, those users at branch F would always use the copy of the files that are more near to them. All files shared in a DFS root would later (at a scheduled time) be synchronized between all DFS roots (2 or more) maintaining a redundant, consistent and fault tolerant Shared resource.
This way you improve bandwidth and make your branch office F user more happy, once they will be working within a DFS root locally.
I have several costumers using this technology with great success. If you have the possibility put this over a w2k3 R2 hosts as they have some nice <i>must have</i> differences from w2k3.
You read something more about this, here.