On fully wild categories of representations of posets

Assume that $I$ is a finite partially ordered set and $k$ is a field. We prove that if the category prin$(kI)$ of prinjective modules over the incidence $k$-algebra $kI$ of $I$ is fully $k$-wild then the category $fpr(I,k)$ of finite dimensional $k$-representations of $I$ is also fully $k$-wild. A key argument is a construction of fully faithful exact endofunctors of the category of finite dimensional $k\langle x,y\rangle$-modules, with the image contained in certain subcategories.