A morphism of supermanifolds is a continuous map and a map of sheaves of superfunctions in the opposite direction. What you've given is the second part of the datum. I guess the continuous map $\mathbb R\to\mathbb R$ between the underlaying manifolds is just the identity.

A morphism of supermanifolds is a continuous map and a map of sheaves of superfunctions in the opposite direction. What you've given is the second part of the datum. In your example, I guess the continuous map $\mathbb R\to\mathbb R$ between the underlaying manifolds is just the identity.