A reflective subcategory of a topos is a topos if the reflector is left exact. Let $H\simeq Sh_J(H)$ be a topos for the canonical topology $J$. Let $$(L\dashv R):E\stackrel{R}{\hookrightarrow} H$$ be the inclusion of a reflective subcategory into a topos. Let $$a:=Sh_J(-):Psh(H)\to H$$ the sheafification functor. $H$ and $E$ are [[total category|total]]. Since $H$ is a topos, $H$ is total, since $E$ is a reflective subcategory of a total category $E$ is total. This implies the the Yoneda embeddings of $E$ and $H$ both posess left adjoints $$(a_H\dashv Y_H):H\hookrightarrow Psh(H)$$ $$(a_E\dashv Y_E):E\hookrightarrow Psh(E)$$ apparently $a_H=Sh_J(H)$. Let $R_!:=Lan_{Y_E} Y_H R$ then we have $L\circ a_H\circ R_!$ is the identity on representables and $$a_E\circ Y_E\simeq L\circ a_H\circ R_!$$ is a natural equivalence.