Torsion-less module over commutative ring whose injective hull is Hopfian

Let $$M$$ be a module over a commutative ring (with unity) $$R$$. Let $$E_R(M)$$ denote the injective Hull of $$M$$ .

If $$M$$ is torsion-less (i.e. $$\cap_{f\in M^*=Hom_R(M,R)} \ker f=(0)$$ ) and $$E_R(M)$$ is Hopfian (i.e. every surjective $$R$$-module homomorphism $$E_R(M) \to E_R(M)$$ is injective), then is $$M$$ Hopfian ? If this is not true in general, what if we assume some more condition on $$R$$ like Noetherian, local ?

If $$R$$ is a commutative integral domain, and $$M$$ is torsion-free, and $$E_R(M)$$ is Hopfian, then I can show that $$M$$ is Hopfian. Since torsion-less is even stronger than torsion-free, hence the question for commutative rings which are not necessarily integral domain.