Summary: We generalize Deng-Du’s folding argument, for the bounded derived category \(\mathcal{D}(Q)\) of an acyclic quiver \(Q\), to the finite-dimensional derived category \(\mathcal{D}(\Gamma Q)\) of the Ginzburg algebra \(\Gamma Q\) associated to \(Q\). We show that the \(F\)-stable category of \(\mathcal{D}(\Gamma Q)\) is equivalent to the finite-dimensional derived category \(\mathcal{D}(\Gamma \mathbb{S})\) of the Ginzburg algebra \(\Gamma \mathbb{S}\) associated to the species \(\mathbb{S}\), which is folded from \(Q\). If \((Q, \mathbb{S})\) is of Dynkin type, we prove that the space \(\mathrm{Stab}\, \mathcal{D}(S)\) of the stability conditions on \(\mathcal{D}(\mathbb{S})\) is canonically isomorphic to the space \( \mathrm{FStab}\, \mathcal{D}(Q)\) of \(F\)-stable stability conditions on \(\mathcal{D}(Q)\). For the case of Ginzburg algebras, we also prove a similar isomorphism between principal components \(\mathrm{Stab}^{\circ}\, \mathcal{D}( \Gamma \mathbb{S})\) and \(\mathrm{FStab}^{\circ}\, \mathcal{D}( \Gamma Q)\). There are two applications. One is for the space \(\mathrm{NStab}\, \mathcal{D} ( \Gamma Q)\) of numerical stability conditions in \(\mathrm{Stab}^{\circ}\, \mathcal{D}( \Gamma Q)\). We show that \(\mathrm{NStab}\, \mathcal{D}( \Gamma Q)\) consists of \(\mathrm{Br}\, Q/ \mathrm{Br}\, \mathbb{S}\) many connected components, each of which is isomorphic to \(\mathrm{Stab}^{\circ}\, \mathcal{D}( \Gamma \mathbb{S})\), for \((Q,\mathbb{S})\) is of type \((A_3,B_2)\) or \((D_4,G_2)\). The other is that we relate the \(F\)-stable stability conditions to Gepner-type stability conditions.