First of all, we find some further properties of the characterization of fiber product preserving bundle functors on the category of all fibered manifolds in terms of an infinite sequence $A$ of Weil algebras and a double sequence $H$ of their homomorphisms from [5]. Then we introduce the concept of Weilian prolongation $W_H^{A}S$ of a smooth category $S$ over $\mathbb{N}$ and of its action $D$. We deduce that the functor $(A,H)$ transforms $D$-bundles into $W_H^{A}D$-bundles.