I'm using VS2013 Update 4 with TFS 2013 Update 4. In Source Control Explorer, whenever I move a file from one folder to another I can see that the file's history is preserved in the new location. However, that history is gone when I check-in the pending changes. The same thing happens when I try to run "tf move" command. So, how can you move a file in TFS and still keep the file's history?
When a file is renamed correctly, the History is not "Gone", it's associated to the "old name" instead. A rename that is done the right way (tracked as a rename and not as an delete+add) has a drilldown option to view the "older" history:
When a rename is done outside of the Source Control Explorer (or from a very old version of the Source Control Explorer (e.g. VS 2008)) or outside the Solution Explorer, then the change will be detected as two individual actions, one delete and one add. You can use the "Pending Changes" window to promote these to a rename so that the history is preserved:
On the commandline this can only be accomplished using "tf rename" and "tf move". Using the standard "mv" and "ren" commands will fail to preserve the history.
Below is a further example of using all the different methods and clearly showing that history is preserved by looking at the history of the current file name:
As mentioned in the comments, history is stored in the Team Project that contains the items revision. When branching/moving across projects your history will be spread across these projects. Should you delete a Team project than all history that was accumulated in that project will be lost.