Nilpotent multiplier of perfect group equals Schur multiplier

Statement
Suppose $$G$$ is a perfect group and $$c$$ is any nonnegative integer. Then, the class $$c$$-nilpotent multiplier of $$G$$ is isomorphic to the Schur multiplier of $$G$$.

Recall that, by definition, the Schur multiplier is the nilpotent multiplier for class $$c = 1$$. 

Journal references

 * , Proposition 2.11