Maybe the mirror is still in Sirius' house. We don't know that he took it to the ministry the night he died. I can't imagine Harry, in his quest to find the other horcruxes not going by Grimmauld Place for a bit... even if it were merely for the protection it might afford him, being unplottable etc. So, most likely he would find the other mirror. Possibly he could leave it in Ron, Hermione, Fred and George or even Kreacher and Dobby's possessions.