In my 2016 book, Rightness as Fairness: A Moral and Political Theory, I argue that morality is a solution to a problem of diachronic rationality called 'the problem of possible future selves.'
To simplify (very) greatly, the problem--which is partially inspired by L.A. Paul's groundbreaking work on transformative experience--is that (A) our present selves have to make decisions on behalf of our future selves, but (B) we do not know which future selves we will actually be (particularly as the future becomes more distant), including (C) what our future selves' retrospective preferences will be regarding our decisions in the present. I then argue that this problem can be solved if and only if our various selves cooperate with each other across time--not just across seconds or minutes, but across decades--to act on principles that are rational for all of one's possible future selves to endorse in unison given mutual recognition of the problem.
The final part of the argument is that this cross-temporal agreement consists of principles of fairness--principles which require one to treat all of one's possible selves fairly, and by extension, all other persons and sentient beings. The reason for this is broadly as follows: because one has an infinite number of possible future selves--some of whom are selfish, others of whom care about other human beings, animals, etc.--the only principles that all of one's selves can rationally agree upon in unison are those that strike a certain kind of compromise between self-interest and the interests of others: a compromise comprised by four principles of fairness.
Anyway, I argue that a rapidly increasing body of neurobehavioral evidence supports picture (a little of which is nicely summarized here and here). In essence, it increasingly appears not only that (A) the neural mechanisms that enable us to care about our own possible future selves just are the neural mechanisms that lead us to care about others, but also that (B) moral behavior and (self-regarding) prudential behavior are simultaneously enhanced or degraded together in direct proportion to the extent to which we concern ourselves with our possible future selves.
Still, all of this is very abstract. Can a simpler, more down-to-earth intuitive case be made for how moral cognition and motivation are rooted in concern for one's possible future (and by extension, possible past) selves? I believe that Christmas parables, of all things, can help!