Was the fire extinguisher invented in 1872?

No, not really. A patent issued that year was entitled "Fire Extinguisher", issued to one Thomas J. Martin, but it was related exclusively to a systems of pressurized pipes installed in buildings for operating sprinklers (or for other purposes).

Such an invention clearly has no relevance to any "portable fire extinguisher", or any other self-contained fire extinguisher, portable or not.