Definition of generalized cohomology with coefficients

Question

I am trying to understand the definition of generalized cohomology with coefficients. Suppose we have a generalized cohomology $E$. Let $p$ be a prime number. Then there is the Moore spectrum $M(\mathbb{F}_p)$, which comes from a cofiber sequence $\mathbb{S} \to \mathbb{S} \to M(\mathbb{F}_p)$, and $E_{\mathbb{F}_p} := E \wedge M(\mathbb{F}_p)$, where $E_{\mathbb{F}_p}$ should be the cohomology theory $E$ with coefficient $\mathbb{F}_p$. I cannot find what exactly the cofiber sequence $\mathbb{S} \to \mathbb{S} \to M(\mathbb{F}_p)$ looks like and what it has to do with the definition of $E_{\mathbb{F}_p}$. Does anybody know what the cofiber map is?