If you have a 15 inch transom, with that transom bracket you should have no need for anything special in order to hang it on your boat.
It should fit a standard transom just fine. Hang it, tighten the thumbscrews, and you should be fine. Tether it with a safety chain to be safe. Most of us don’t do that nearly often enough, myself included.
pay attention to the advice about verifying that the lower unit swing, and enjoy the ride.
best,
PM T2