Git detects renames rather than persisting the operation with the commit, so whether you use git mvor just a plain mv doesn't matter.
The log command, however, takes a --follow argument that continues history before a rename operation (that is, it searches for similar content using the heuristics):
http://git-scm.com/docs/git-log
To lookup the full history use the following command:
git log --follow ./path/to/file