Gruslys, Leader and Tan's hypercube edge-packing conjecture

Let $Q_k$ denote the $k$-dimensional hypercube, and let $H$ be a non-empty subgraph of $Q_k$. An edge-packing by $H$ is a collection of edge-disjoint copies of $H$.

Gruslys, Leader and Tan's conjecture. For $kge 1$, there exists a positive integer $n$ such that the edges of $Q_n$ can be covered by edge-disjoint copies of $H$; the copies of $H$ are not required to be induced.

This is an edge-packing analogue of the vertex-packing results for hypercubes. The supplied text gives no resolution status for this conjecture.