On lifting of connections to Weil bundles

We prove that the problem of finding all Mf(m)-natural operators B : Q -> QT(A) lifting classical linear connections del on m-manifolds M to classical linear connections B-M(del) on the Weil bundle (TM)-M-A corresponding to a p-dimensional (over R) Weil algebra A is equivalent to the one of finding all Mf(m)-natural operators C : Q -> (T-p-1(1),T*circle times T*circle times T) transforming classical linear connections V on m-manifolds M into base-preserving fibred maps C-M(del) : (Tp-1M)-M-1 = circle plus(p-1)(M) TM -> T*M circle times T*M circle times TM.