I'm not really sure Adorno thinks there is any relation between art and morality to be honest - what he does think is that art holds open the possibility of unalienated labour and therefore an image of a utopia, which, for Adorno, is the narrowest of pinpricks of light in the overwhelming bleakness of instrumentalised existence. This is as close as he gets to a version of Kant's aesthetic 'moral image ofthe world' Jay Bernstein may have something to say on the subject in his Ethics of Disenchantment; I'll check when i get home...
Adorno's Aesthetic Theory works as a sort of negative of Kant; whereas for Kant, the act of aesthetic judgment has as its subject, the judgment itself, with its moments of disinterest, purposiveness without purpose, universality and necessity, for Adorno, these moments migrate into the work itself, which stands as an exemplar of non- identity, of the primacy of the object, of that which escapes the clutches of instrumental reason (and therefore of capital).
Bernstein argues that there is an ethics to be read in Adorno, and certainly, one cannot read him without feeling a powerful moral force underneath; but its really difficult to actually state what that moral or ethical position might be; it's too easy to reduce Adorno to caricature, to the straw man of cult. studs. - he hated jazz (boo!) - or a few quotes 'no poetry after Auschwitz' and so on; his method certainly doesn't help...
I'll try and dig up a bit more later, if you like; how much and in how much detail do you need?