Lubin–Tate formal module in a cyclic unramified $p$-extension as Galois module

In this paper we describe the structure of the $\mathcal O_K[G]$-module $F(\mathfrak m_M)$, where $M/L$, $L/K$, $K/\mathbb Q_p$ are finite Galois extensions ($p$ is fixed prime number), $G=\mathrm{Gal}(M/L)$, $\mathfrak m_M$ is a maximal ideal of $M$ and $F$ is a formal Lubin–Tate group law over $\mathcal O_K$ for a prime element $\pi$.