EN
We classify all $ℱℳ_{m,n}$-natural operators $𝓓 :J² ⟿ J²V^{A}$ transforming second order connections Γ: Y → J²Y on a fibred manifold Y → M into second order connections $𝓓(Γ): V^{A}Y → J²V^{A}Y$ on the vertical Weil bundle $V^{A}Y → M$ corresponding to a Weil algebra A.