Finite-type reformulation of the telescope conjecture for module categories

Let $\Lambda$ be an artin algebra, and let $(\mathcal{A},\mathcal{B})$ be a hereditary cotorsion pair in the category of all left $\Lambda$-modules. A cotorsion pair is of finite type if $\mathcal{B}=\operatorname{Ker}\operatorname{Ext}^1_\Lambda(\mathcal{S},-)$ for a set $\mathcal{S}$ of finitely generated modules; assume that $\mathcal{B}$ is closed under direct limits. The finite-type reformulation. The cotorsion pair $(\mathcal{A},\mathcal{B})$ is of finite type. The source says this is equivalent to the preceding module-category formulation, using an external result; its resolution is not given in the supplied text.