In the web page http://www.encyclopediaofmath.org/index.php/Moore_space it can be found the following statement:

If $K(\mathbb Z,n)$ is the Eilenberg–MacLane space of the group of integers $\mathbb Z$ and $M_k(G)$ is the Moore space with $\tilde{H}_k(M_k(G))=G$, then

$$lim_{N\rightarrow\infty}[\sum^{N+k}X,K(\mathbb Z, N+n)\bigwedge M_k(G)]\cong H^n(X,G)$$,

that is, $\{K(\mathbb Z\wedge M_k(G)\}$ is the spectrum of the cohomology theory $H^*(\ ,G)$.

The reference of the webpage is the articule of Moore ´´On homotopy groups of spaces with single non-vanishing homotopy group´´ but I don´t find anything like that on the article.

It would be very helpful if you could give a reference where I can see the explanation or you can explain me that.

In the web page http://www.encyclopediaofmath.org/index.php/Moore_space it can be found the following statement:

If $K(\mathbb Z,n)$ is the Eilenberg–MacLane space of the group of integers $\mathbb Z$ and $M_k(G)$ is the Moore space with $\tilde{H}_k(M_k(G))=G$, then

$$lim_{N\rightarrow\infty}[\Sigma^{N+k}X,K(\mathbb Z, N+n)\bigwedge M_k(G)]\cong H^n(X,G)$$,

that is, $\{K(\mathbb Z,n)\wedge M_k(G)\}$ is the spectrum of the cohomology theory $H^*(\ ,G)$.

The reference of the webpage is the articule of Moore ´´On homotopy groups of spaces with single non-vanishing homotopy group´´ but I don´t find anything like that on the article.

It would be very helpful if you could give a reference where I can see the explanation or you can explain me that.