Well yes, let's see if I can write something off the top of my head, make it clear and readable at the same!
...this is going to be long...
First, I do agree with your broad interpretation of "society" and "social interactions". The nuances when discussing animals in generals and human society is important; I'll come back to this later.
To answer your question directly, I guess that with the notion of 'society' comes 'morality', thus morality would technically precede homo sapiens. This isn't all that big a deal for the following reasons:
* When I think of society and morality, I do indeed think 'executive function and processing with relation between self and others'. As in this is a necessary (and sufficient) part of both, hence society necessarily entails morality. They kinda form at the same time and end up being mutually interdependent.
* These taxonomical labels and chronologies aren't exactly the most concrete thing in the world; they're defined by sufficient divergence in characteristics (this relates to the whole 'human' thing, but it's essentially more of a side note), and since evolution and adaptation is a continual process, there's obviously going to be an element of incompatability.
* I would reject that animals "do not possess any executive functioning, unlike humans". To claim this would be to say that animals are biological machines- from my previous post I find it difficult to say that and then reject the same claim for humans, and since I find it more useful to reject incompatiblist determinism for humans...you see where this is going?
* Hence I'd rather consider animals agents in their own right- it is then a matter of coming to understand the manner in which they go about their ways, not to mention interspecies interactions (including, or especially with humans). Obviously they are different from humans- on that note, it seems to me that what is uniquely human, I could loosely describe as metaphysical querying, supported by the degree of the formation of our language.
So from all the above, I get this: we can claim that the animals whose behaviors we can recognise share the same fundamental structure have a form of 'society' and 'morality'. Exactly how this manifests with them would be unique to them, just as the way we discuss society and morality as humans is unique to us. In this case, because of our empahsis on cognisation, the scope of morality has acheived a level of abstraction that we observe in cultural theatres.
But I would still say it stemmed from our 'organic capabilities', in a sense- again, it's difficult to avoid slipping between the interpretations of "we are different to other animals".
So...yeah, seeing as much of the evidence I've alluded to as support for the arguments I present are retrospective, the connection was probably made before we arrived on the scene, but it was only represented, articulated and debated after we arrived on the scene.
I have a few examples up my sleeve if need be, but this post is probably too long as it is.