2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125052Recently we found that canonical gauge-natural superpotentials are obtained as global sections of the {\em reduced} $(n-2)$-degree and $(2s-1)$-order quotient sheaf on the fibered manifold $\bY_{\zet} \times_{\bX} \mathfrak{K}$, where $\mathfrak{K}$ is an appropriate subbundle of the vector bundle of (prolongations of) infinitesimal right-invariant automorphisms $\barΞ$. In this paper, we provide an alternative proof of the fact that the naturality property $\cL_{j_{s}\barΞ_{H}}ω(λ, \mathfrak{K})=0$ holds true for the {\em new} Lagrangian $ω(λ, \mathfrak{K})$ obtained contracting the Euler--Lagrange form of the original Lagrangian with $\barΞ_{V}\in \mathfrak{K}$. We use as fundamental tools an invariant decomposition formula of vertical morphisms due to Kolář and the theory of iterated Lie derivatives of sections of fibered bundles. As a consequence, we recover the existence of a canonical generalized energy--momentum conserved tensor density associated with $ω(λ, \mathfrak{K})$.16 pages, abstract rewritten, body slightly revised, Proc. Winter School "Geometry and Physics" (Srni,CZ 2005)Mathematical Physics58A20; 58A32; 58E30; 58E40; 58J10; 58J70text