Hasunuma's edge-removable tree conjecture

For $k\ge 1$, let $T$ be a tree of order $m$, and let $G$ be a $k$-connected or $k$-edge-connected graph with minimum degree $\delta(G)\ge k+m-1$. A subtree $T'$ is isomorphic to $T$ when $T'\cong T$. Hasunuma's edge-removable tree conjecture. The graph $G$ contains a subtree $T'\cong T$ such that deleting the edges of $T'$ leaves $G-E(T')$ $k$-connected in the vertex-connectivity case, or $k$-edge-connected in the edge-connectivity case. This is an edge-removable analogue of Mader's tree-removability conjecture; the supplied context does not state a resolution, so its general status remains open.