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In this paper we consider proper holomorphic embeddings of finitely connected planar domains into ℂn that approximate given proper embeddings on smooth curves. As a side result we obtain a tool for approximating a $\mathcal{C}^{\infty}$ diffeomorphism on a polynomially convex set in ℂn by an automorphism of ℂn that satisfies some additional properties along a real embedded curve.