Flat hypercomplex nilmanifolds are H-solvable

We say that a hypercomplex nilpotent Lie algebra is $\mathbb{H}$-solvable if there exists a sequence of $\mathbb{H}$-invariant subalgebras ${\mathfrak{g}}_1^{\mathbb{H}}\supset {\mathfrak{g}}_2^{\mathbb{H}}\supset \cdots \supset {\mathfrak{g}}_{k-1}^{\mathbb{H}}\supset {\mathfrak{g}}_k^{\mathbb{H}}=0,$ such that $[{\mathfrak{g}}_i^{\mathbb{H}},{\mathfrak{g}}_i^{\mathbb{H}}]\subset {\mathfrak{g}}_{i+1}^{\mathbb{H}}\mathrm{.}$ Let $N=\mathrm{\Gamma }\mathrm{\backslash }G$ be a hypercomplex nilmanifold with flat Obata connection and $\mathfrak{g}=Lie(G)$. We prove that the Lie algebra $\mathfrak{g}$ is $\mathbb{H}$-solvable.