The production of pairs of correlated Lyman-alpha photons upon XUV excitation of molecular hydrogen is studied using coincidence measurements to evaluate at which level the entanglement is transferred from atoms to photons. By referencing the timing of fluorescence photon detection to the synchrotron light pulse, we were able to determine branching ratios for the 2p + 2p and 2p + 3 (with = s, d) channels separately. Time-dependent analysis of the spectral signature recorded around 33.6 eV and close examination of the doubly excited states lying in the Franck-Condon window confirm prior assignments of the 2p + 2p being the main dissociation channel of the Q2 1 pi u (1) molecular state. The angular dependence of the two-photon detection probability measured with respect to the polarization axis is found to be in agreement with earlier measurements [Y. Torizuka et al., Phys. Rev. A 99, 063426 (2019)]. A simple model, assuming a transition from Hund's case (a) to Hund's case (c), reproduces the measured angular distributions satisfactorily.