Strong Lefschetz conjecture for Jacobian algebras of smooth hypersurfaces

Let $S=\mathbb{C}[x_0,\ldots,x_n]$ be the graded polynomial ring in $n+1$ variables, with $n\geq 2$, and let $f\in S_d$ be a homogeneous polynomial such that the hypersurface $V(f):f=0$ in $\mathbb{P}^n$ is smooth. Writing $M(f)=S/J(f)$ for its Jacobian algebra, where $J(f)$ is generated by the partial derivatives of $f$, the algebra $M(f)$ is Artinian graded Gorenstein. Strong Lefschetz conjecture for Jacobian algebras. The Jacobian algebra $M(f)$ has $SLP$ for any polynomial $f\in S_d$ such that $V(f)$ is smooth. Since Fermat-type Jacobian algebras have $SLP$ and the property is semicontinuous, this is known for a generic polynomial, while the conjecture asks for the property for every smooth hypersurface.