I am sorry to hear about your son. This is very difficult news to hear.
There is no relationship between Asperger's Syndrome, which is a pervasive developmental disorder, and Schizophrenia, a psychotic disorder. They are completely different issues. One does not cause the other, although it is possible to have both at the same time.
Could your son have had schizophrenia as a child? It is possible, but it is not typical. This disorder, schizophrenia, is not common as a childhood onset. It can occur, but it is very rare. Schizophrenia occurs mostly between 17-25 years of age as an onset.
Although schizophrenia is a difficult disorder, there are excellent medications to treat the psychotic thinking. Therapy can also help Asperger's Disorder and there is a good chance that your son can be rid of his psychotic symptoms and will stabilize. Steven