  Stanley introduced and studied two lattice polytopes, the order polytope and
chain polytope, associated to a finite poset. Recently Ohsugi and Tsuchiya
introduce an enriched version of them, called the enriched order polytope and
enriched chain polytope. In this paper, we give a piecewise-linear bijection
between these enriched poset polytopes, which is an enriched analogue of
Stanley's transfer map and bijectively proves that they have the same Ehrhart
polynomials. Also we construct explicitly unimodular triangulations of two
enriched poset polytopes.
