Oh, they do.
Studies show that many animals are capable of complex reasoning when it comes to moral choices. Their level of understanding in social relations and forms of 'trade' is very advanced.
Now, humans have always hidden behind our intellect, to claim our uniqueness and therefore to be excused in how we deal with animals.
It would be weird to say that, now animals appear to have an intellect that's often even pretty advanced, it would actually be our instincts, that make us morally aware. Because instincts among animals have been acknowledged all along.
Morality is a mixture of instincts and intellect, and both animals as humans have that combination.