This might sound crazy and most probably there is a better solution.
This should write all commit hashes doing changes to this folder into the file all-the-commits
.
Then create a new orphan branch (meaning that it does not have any parent commits)
git checkout --orphan <new-branch-name>
Then cherry-pick all those commits you obtained onto this new branch
cat <all-the-commits> | xargs -n 1 git cherry-pick
Check and correct the current working directory
Last but not least create a new repo and push this single branch to the other repository
git push <new-repo> <new-branch-name>
The end result should be, that in the new repository you have only files from you subproject together with all commits that changes files in this folder (and only those commits).
I had no chance to test these steps, if this sounds like a viable solution I will check and elaborate more if needed.