Brough–Eick conjecture on contact and Hamiltonian algebra quotients

Let $\mathbb F$ be a field of characteristic $2$. Let $n\in\mathbb N$ be odd, $m\in\mathbb N^n$, and set $K=K(n,m)$. Write $K'$ for the derived algebra and $N(K')$ for its relevant maximal nilpotent ideal; likewise write $N(H)$ for the corresponding ideal of $H=H(n-1,(m_1,\ldots,m_{n-1}))$. Brough–Eick's quotient-isomorphism conjecture. The quotient $K'/N(K')$ is simple and isomorphic to $H/N(H)$:

$$K'/N(K')\cong H/N(H),\qquad H=H(n-1,(m_1,\ldots,m_{n-1})).$$

The conjecture is based on computational evidence and concerns the expected simple Hamiltonian quotient associated with each odd-dimensional contact algebra.