Migrating from LocalFSProvider to GitFSProvider and vice versa should be seamless.
GitFSProvider ensures that tasks and course are versioned with Git repositories, creating them if they do not exist.
On the other hand, LocalFSProvider ignores .git directories.

However, we still have to asses some migration issues:

1. If the $common directory already exists, it must be turned into a git repository, then added as a submodule to the course and each course's task. This migration is currently not handled in Storing courses and tasks in Git repositories #1058.
2. Each user with write access to courses now requires a private SSH key. After discussing with @anthonygego, we agreed that adding a migration script directly interacting with deployment databases would be the most straightforward way to handle such addition. This script should also push the added keys to deployment gitolite instances.
3. Some existing courses are already versioned with git outside of INGInious. The remotes of such courses won't point to the INGInous gitolite instance and the SSH key stored by INGInious will not allow access to external remotes such as GitHub or Gitlab.