I found an open-source project which is available via hg only.
Now I want to put it onto GitHub, with my own changes alongside the previous commit history.
Hg-git allows you to use git commands to push to hg (Mercurial).
Setup your environment (once Python 2.7.*+Mercurial 2.2 are installed)
Clone your hg repo
Push that to Github (or other git host)
Side note (unrelated):
is wrong impression - hg-git allow Mercurial client interact (bidirectionally) with remote Git-reposiory and can be used (if you have Mercurial) - pull from hg + push to Git