I'm struggling with the term 'moral fact'. Not in a combative way, but I wonder what the definition would be.
'Morality is biological' sounds like a claim where the truth would depend on your definition of an array of terms. On the one hand I could see if we we take a loose definition of morality then it's clear that behavior with moral implications emanates from biological reality. On the other hand, if we wanted to get annoyingly pedantic we'd have to ask ourselves what the word morality actually means. It seems intuitively obvious, but when you look deeper it really isn't.
There is a colloquial definition of the term which allows the every-day person to converse and easily find common meaning, make contrasts, comparisons, and judgements, but then we come back to the phrase.. moral fact. What is a moral fact and what would be it's source? If there can be moral facts, then there can be a formal definition of what is moral, but this is where I get hung up. I've only ever seen moral behavior as something that is strictly relative and subjective, so from what I can see there can only be moral interpretation, not moral fact.
Sounds annoyingly pedantic, and maybe it is, but this points to the importance of definitions in clarifying our thoughts. If we can agree that there is no such thing as a moral fact, then what is morality, and what is it's connection with biology? I'd argue that you can have a biological fact, and that a biological fact produces behavior with moralistic implications, but in practice there is no tangible connection with something called 'morality'. Morality is an interpretation of biological behavior in retrospect, and a social source of determining our courses of action. Our biology sets the framework, our behavior emanates from our biology and is constrained by institutionalized moral codes, but morality is only ever a useful description which we use in every-day discourse. So at most we can say something like 'there is behavior', or 'there is behavior which we interpret based on social code', or 'moral code springs forth from biology'. But in the strictest sense of the term the phrase 'morality is biological' doesn't seem coherent. The problem is ultimately that we're thinking about morality as something with a concrete existence, rather than a fluid aspect of culture.
That all sounds complicated but instead of writing a 500 page book like most philosophers would do, instead I'd simplify it all and say that 'morality' is just a construct of language which we use to define, judge, and control behavior. Inevitably the codes we use to judge behavior look biological, because what else would they look like, but at best they're a set of ever changing guidelines rooted in culture, with our biology as a framework.
All of that said it's just as easy to go back to the loose definition of morality and say that our moral codes are rooted in biology and leave it at that. This just leaves the term 'morality', and what is moral somewhat ambiguous.
One way to at least narrow down the focus, I'm suggesting, and potentially cut through some of the crap and confusion, as it were, would be to consider the example rule or fact in the OP,
"continued existence is right" (or is good, or is suitable, or desirable, or works for me, or whatever) specifically 'my/our' existence. This at least appears to be unchanging, independent of culture and even species, and applies to or is applied by (sometimes instinctively or automatically, sometimes not) all living things, and possibly even genes, anywhere, and as far as we can tell always has (with some exceptions in certain circumstances) and is therefore at least a biological rule, literally a fact of life, like having two hands is for certain species. We could think of it, perhaps, as a fundamental drive, which is, usefully, a 'mechanical' term, and of course drives (and even desires, assuming they are not effectively the same thing or very similar) don't have to be consciously-experienced, they can exist without that add-on feature.
Granted, we may need a more-extended-than-usual definition of morality to call it a moral rule or fact, but in the end the point might be that it answers the question
"what is moral?" with
"(my/our) continued existence", so maybe extending the definition is warranted. It may be that everything about 'right' and 'wrong', and/or what is considered to be either of those, follows from it and/or is merely commentary on it, for humans, chimps, poodles, fish, beetles, didiniums, daffodils and lichens. And an organism or species doesn't have to have sophisticated (or indeed any) mental experiences of or about the rule, such as 'feeling good' about it, though some will, and others won't, possibly because the latter merely lack the biological structures that allow the capacity to have experiences associated with their own behaviours, in this case alongside the operation of the rule, the rule that answers the question, 'what is moral' and by short extension 'what is morality?'