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Let $g:A\to B$ be a finite partial elementary map in $M$. In a countable language, the algebraic closures of finite sets are countable. An alternating back-and-forth construction extends $g$ to an isomorphismAt each step, an element algebraic over the current domain has a finite algebraic type, and elementarity provides a matching realization on the other side.

Choose a basis of a pregeometry $C$ over the first closed set and a basis of a pregeometry $D$ over the second. The dimension of a pregeometry is the same for the two extensions: the isomorphism preserves the finite ranks already contributed by $A$ and $B$, while both sides have the same ambient dimension. Choose a bijection $C\to D$. Part (a) and uniqueness of the generic type in a strongly minimal theory make the enlarged map elementary. Since an elementary submodel is algebraically closed in the monster,and the map extends over algebraic closure to an automorphism of $M$. Thus every finite partial elementary map extends to an automorphism: every model is homogeneous, as stated in homogeneity of models of a countable strongly minimal theory.