Ramification estimate for Fontaine-Laffaille Galois modules

Suppose $K$ is unramified over $\mathbb Q _p$ and $\Gamma _K=\operatorname{Gal}(\bar K/K)$. Let $H$ be a torsion $\Gamma _K$-equivariant subquotient of crystalline $\mathbb Q _p[\Gamma _K]$-module with HT weights from $[0,p-2]$. We give a new proof of Fontaine's conjecture about the triviality of action of some ramification subgroups $\Gamma _K^{(v)}$ on $H$. The earlier author's proof from [1] contains a gap and proves this conjecture only for some subgroups of index $p$ in $\Gamma _K^{(v)}$.