I agree with you that we are an extension, although I would prefer a term like hologram. So in one sense we are not separated from God, but on the whole, or at least for most people, we experience ourselves as being separated. So when I say work, I don't mean ‘working to remember’, although that is also important, rather understanding the meaning of this particular incarnation, the task we have been chosen to perform. We are working for society and the world, as much as we are working on ourselves.
The Hindu concept of Karma Yoga seems to describe this as well as anything.