  We study the photoproduction of a D^{*+-} meson in association with a hadron
jet at next-to-leading order in the parton model of QCD with non-perturbative
fragmentation functions extracted from LEP1 data of e^+e^- annihilation. The
transverse-momentum and rapidity distributions recently measured at DESY HERA
in various kinematic ranges nicely agree with our theoretical predictions. This
provides a useful test of the universality and the scaling violations of the
fragmentation functions predicted by the factorization theorem. These
comparisons also illustrate the significance of the charm component in the
resolved photon. This is elaborated by investigating the cross-section
distributions in x_obs^gamma and cos(theta^*).
