Let's go with their meeting in the immediate aftermath in Ryouma's Sutoku post, just to keep forward momentum! If she hits up his comment there they can immediately get into potential post-investigation paths, their suspicion of the faction shenanigans in general, AND the fact that he is a stupid idiot and should not be drinking excessively to cope with getting shot. Efficiency at its finest.

For actual investigation, since the sewers are blocked for April, I just asked about Alliance members questioning the Kappa workers! So they could maybe pursue that, or we can come up with a different investigation angle if you like? So many mysteries, so little time.