Let $\mathbf A$ be a dg-category. Denote by $\mathsf{C}_{\mathrm{dg}}(\mathbf A)$ the dg-category of right $\mathbf A$-modules, and by $\mathsf{C}(\mathbf A) = Z^0(\mathsf{C}_{\mathrm{dg}}(\mathbf A))$, its underlying category (which is endowed with the projective model category structure). Moreover, set $\mathsf{K}(\mathbf A) = H^0(\mathsf{C}_{\mathrm{dg}}(\mathbf A))$, the homotopy category of modules, and let $\mathsf{D}(\mathbf A)$ be the derived category of $\mathbf A$, that is, the localisation of $\mathsf{K}(\mathbf A)$ (or, equivalently, of $\mathsf{C}(\mathbf A)$) along quasi-isomorphisms. Denote by $\delta \colon \mathsf{K}(\mathbf A) \to \mathsf{D}(\mathbf A)$ the localisation functor. The machinery of model categories tells us that, if $P \in \mathsf{C}(\mathbf A)$ is a cofibrant dg-module, then, for any dg-module $M$, the localisation functor induces an isomorphism \begin{equation} \mathsf{K}(\mathbf A)(P, M) \xrightarrow{\sim} \mathsf{D}(\mathbf A)(P,M). \end{equation}

The question is: is the above result true if $P$ is a h-projective dg-module? By definition, $P$ is h-projective if, whenever $A$ is an acyclic dg-module, the hom-complex $\mathsf{C}_{\mathrm{dg}}(\mathbf A)(P, A)$ is acyclic. Notice that a cofibrant dg-module is also h-projective.