I wanted to move a directory from one repo to another, keeping the commit history and without introducing new noise to the commit history. Summarizing what I've learned from a few different sources, here's how I accomplished it.
Let's say we want to move only "dir/directory_src" of "repo_one" to "dir/directory_dest" of "repo_two" (using a shell in Linux):
Now let's copy the files into repo_two.
"repo_two" should now contain "dir/directory_dest" and all of its contents.
Note: when using the filter to remove other files outside of the directory might keep files around if the names that contain spaces or tabs.