I added a GitHub-based library as a submodule and modified it. I need to share the modification with my teammates.
- I won't be able to push it to submodule's GitHub origin, would I?
No: you need to fork that GitHub project first, and add that fork as a submodule.
(or change the current submodule url by the one of your fork)
- How do I share the modification?
Once you have added your fork as a submodule, you will be able to push modification to its upstream repo.
- I'm not supposed to modify submodules which I get from GitHub?
Submodule or not, you cannot modify GitHub repos you are not the owner (or a declared collaborator) of.