Proper holomorphic embeddings into strictly convex domains

Assume that is a $$\varOmega $$ bounded, strictly pseudoconvexed domain with $$C^{2}$$ boundary. Let $$D\subset \mathbb {C}^{n}$$ be a bounded strictly convex domain in a geometric sense, i.e. D is bounded and convex without any line segment in the boundary. If n is large enough, then there exists a proper holomorphic embedding $$f:\varOmega \rightarrow D$$ , which extends continuously through $$\overline{\varOmega }$$ .