The Telescope Conjecture for smashing subcategories

Let ${\mathbf{T}}$ be a compactly generated triangulated category with small coproducts, and let ${\mathbf{L}}$ be a smashing subcategory of ${\mathbf{T}}$, meaning that the inclusion ${\mathbf{L}}\hookrightarrow {\mathbf{T}}$ has a right adjoint commuting with small coproducts. Write ${\mathbf{T}}^c$ and ${\mathbf{L}}^c$ for the compact objects.

Telescope Conjecture. Then

$${\mathbf{L}}^c={\mathbf{L}}\cap{\mathbf{T}}^c$$

and ${\mathbf{L}}^c$ satisfies (G1) in ${\mathbf{L}}$.

This is stated as the converse to the preceding lemma, which shows that the condition on compact objects implies that the subcategory is smashing. The source gives no resolution of this conjecture.