G.E. Reyes, Embedding manifolds with boundary in smooth toposes, Cahiers de Top. et Geom. Diff. Catég., (48), 83-103, (2007). We embed fully and faithfully the category of manifolds with boundary in some “smooth” toposes. We show that the embedding preserves open coverings and some products. Furthermore, it sends a Weil’s prolongation of a manifold by a Weil algebra into the embedded manifold raised to the associated infinitesimal space of the algebra. Our main tool is to “double” the manifold with boundary to obtain one without boundary.