The free Lie-module generator conjecture for the cyclic Lie sub-operad of PreLie

Let $\operatorname{PreLie}$ be the PreLie operad and let $M$ be the sub-operad generated by the image of $\operatorname{CycLie}$ under the injective map $\lambda$. The composition $\circ$ is composition of $\mathfrak{S}$-modules, and $\operatorname{Indec}$ denotes the indecomposable module used in the paper. The free Lie-module generator conjecture. The sub-operad $M$ is a module of generators of $\operatorname{PreLie}$ as a free left $\operatorname{Lie}$-module, namely

$$\operatorname{PreLie}\simeq\operatorname{Lie}\circ M$$

and

$$M\simeq\operatorname{Indec}.$$

The claim would identify the explicitly constructed cyclic-Lie sub-operad as the generator module in the known free left Lie-module structure of PreLie; the source gives no resolution.