I have a basic question on Voevodsky's stable homotopy category of spectra $\mathbf{SH}(S)$, where $S$ is a finite dimensional noetherian scheme.

Let $E$ be an $\Omega$-spectrum and $\varphi \colon F\to E$ be a morphism of spectra satisfying that for any smooth $S$-scheme $X$ the induced map
$$
\mathrm{Hom}_{\mathbf{SH}(S)}(X,F)\longrightarrow \mathrm{Hom}_{\mathbf{SH}(S)}(X,E)
$$
is an isomorphism of groups. The question is: **Is $\varphi\colon F\to E$ an isomorphism of spectra?**