No, leaf is wrong, black mulberry leaves are much more toothed than that, and less lobate, and have a thicker stem. Also black mulberries mostly aren't black, most of them fall off before they get that dark, hence the term "mulberry coloured". Mine still has lots of berries on it - they ripen over a long period, I've been picking them since early August. I think you'd notice if you had a mulberry tree.