Embedding of moduli space of J-holomorphic spheres into moduli space of stable maps

Question

Let $(M,\omega)$ be a closed symplectic manifold of dimension $2m$, $J$ be an $\omega$-compatible almost complex structure, and $A\in H_2(M;\mathbb{Z})$ a homology class. Let $n \geq 3$ and denote by $\mathcal{M}_{0,n}(A;J)$ be the moduli space of $J$-holomorphic spheres and $\overline{\mathcal{M}}_{0,n}(A;J)$ the moduli space of stable $J$-holomorphic maps (of genus zero) representing $A$. I am wondering whether the inclusion $\mathcal{M}_{0,n}(A;J)\rightarrow \overline{\mathcal{M}}_{0,n}(A;J)$ induces an isomorphism in compactly supported $\check{C}$ech cohomology in the degree of the virtual dimension?