= Solution
In a <strongly minimal theory>, <model-theoretic algebraic closure> is a <pregeometry>. If $C$ is algebraically closed, every element outside $C$ realizes the <generic type in a strongly minimal theory>: every one-variable definable set is finite or cofinite, and a point outside $C$ belongs to none of the finite ones.
Enumerate a finite tuple $a_1,\ldots,a_n$ of distinct elements of the independent set $A$. Independence says
$$
a_i\notin\operatorname{acl}(a_1,\ldots,a_{i-1}).
$$
Its image tuple under the bijection has the same property. Inductively, $a_i$ and $f(a_i)$ realize the same generic type over the algebraic closures of the preceding tuples, so every finite restriction of $f$ is elementary. First-order formulas involve only finitely many parameters, hence the entire bijection is an elementary map. This is the <independent set in a strongly minimal theory> principle.
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