(informal) Is the boundary of locally conformally flat Manifold also locally conformally flat

Question

Just a quick informal Question. I was wondering if the boundary of an LCF Manifold is also LCF ? By definition a LCF manifold is one in which, for each point, there exists a neighborhood around that point that can be conformally transformed to a flat Euclidean space. Since the boundary is a submanifold the answer to the above question should be, yes ! Do I have to be careful to which EUclidean Space i send the conformal transformation? i.e should boundary points only be conformally mapped to an euclidean half space? Thanks for clarification!