  Let $\mathcal{M}$ be an $n$-cluster tilting subcategory of ${\rm
mod}\mbox{-}\Lambda$, where $\Lambda$ is an artin algebra. Let
$\mathcal{S}(\mathcal{M})$ denotes the full subcategory of
$\mathcal{S}(\Lambda)$, the submodule category of $\Lambda$, consisting of all
monomorphisms in $\mathcal{M}$. We construct two functors from
$\mathcal{S}(\mathcal{M})$ to ${\rm mod}\mbox{-}\underline{\mathcal{M}}$, the
category of finitely presented (coherent) additive contravariant functors on
the stable category of $\mathcal{M}$. We show that these functors are full,
dense and objective. So they induce equivalences from the quotient categories
of the submodule category of $\mathcal{M}$ modulo their respective kernels.
Moreover, they are related by a syzygy functor on the stable category of ${\rm
mod}\mbox{-}\underline{\mathcal{M}}$. These functors can be considered as a
higher version of the two functors studied by Ringel and Zhang [RZ] in the case
$\Lambda=k[x]/{\langle x^n \rangle}$ and generalized later by Eir\'{i}ksson [E]
to self-injective artin algebras. Several applications will be provided.
