How to migrate part of a Drupal project to a new project repository

This is a writeup of a problem I encountered when working on the CollectiveAccess Drupal module: I had been maintaining a submodule called CollectiveAccess Feeds within the main Drupal CollectiveAccess project, but I found out that it would be more practical to have this as a separate module, in order to move it faster then the CollectiveAccess module itself, which is already more stabilized. Continue reading to see the steps I took to migrate this module to a new Drupal project.