Be careful to not conflate morality itself with moral behavior or attitudes.
Talk of "morality" refers to properties such as goodness, evilness, rightness, wrongness, virtuousness, viciousness, and so on. It does not refer to the patterns of behavior that we typically deem good, or to opinions about what is good, or the like.
Craig think that moral properties are ontologically dependent on God, or that they are in some way constituted of theological properties (e.g., being commanded by God, or being in some way or anther like God). Craig does not think that we need God to be good people or behave morally, or that we need God to have beliefs about morality or knowledge of morality. And while Craig does think that God is responsible for our being moral and our ethical attitudes, this is only because he thinks that God is responsible for everything in creation. But it is perfectly consistent with his argument that God is not responsible for giving us our patters of moral behavior, or our attitudes about morality.