According to Catholic doctrine, would a cloned human being have a soul?

Recently I heard from my devout religious acquaintance that, according to Christian (Catholic) faith, a cloned individual wouldn't actually be a person. She explained that a human being consists of a body and a soul (it's the philosophy of St Thomas, the conception is derived form Aristotle, I suppose). As the flesh can be created by scientists, only God can grant something (somebody) with a soul. As cloning is — according to her — an artificial way of creating a man, you can't divide the spirit like you can split the cells. So I’m asking you a question: Is this really part of Catholic ethics? I understand that the Church is against cloning, but this is the first time I’ve heard that the “effect” of it is, so to say, punished. The same could apply to *in vitro* conception, but I suppose cloning could be taken as a more radical version of this.