Ideals_Containing_Ideal_Isomorphic_to_Quotient_Ring

Let $J$ be an ideal of a ring $R$. Let $\mathbb L_J$ be the set of all ideals of $R$ which contain $J$. Let the ordered set $\left({\mathbb L \left({R / J}\right), \subseteq}\right)$ be the set of all ideals of $R / J$. Let the mapping $\Phi_J: \left({\mathbb L_J, \subseteq}\right) \to \left({\mathbb L \left({R / J}\right), \subseteq}\right)$ be defined as $\forall a \in \mathbb L_J: \Phi_J \left({a}\right) = q_J \left({a}\right)$ where $q_J: a \to a / J$ is the quotient epimorphism from $a$ to $a / J$ from the definition of quotient ring. Then $\Phi_J$ is an isomorphism.