Keller–Pilpel's influence conjecture for monotone Boolean functions

Let $f:\{0,1\}^n\to\{0,1\}$ be an $n$-variable monotone Boolean function, and let $L\in GL_n(\mathbb{F}_2)$ be an invertible linear transformation. Define

$$(Lf)(x)=f(Lx).$$

Keller–Pilpel's conjecture. The total influence of $f$ should satisfy

$$I(f)\leqslant I(Lf).$$

The conjecture asks whether applying any invertible linear transformation over $\mathbb{F}_2$ can only increase the total influence of a monotone Boolean function. It was raised by Keller and Pilpel; the supplied source does not establish its resolution.