The natural operators of general affine connections into general affine connections

We reduce the problem of describing all $\mathcal{M}{f}_m$-natural operators  transforming general affine connections on $m$-manifolds into general affine ones to the known description of all $GL({\mathbf{R}}^m)$-invariant maps ${\mathbf{R}}^{m\ast }\otimes {\mathbf{R}}^m\to {\otimes }^k{\mathbf{R}}^{m\ast }\otimes {\otimes }^k{\mathbf{R}}^m$ for $k=1,3$.