What adapter do I need to connect Mr. Heater F273704 to a LP gas tank that has
The left-side connector on the upper hose is called POL. The connector on the lower hose is called ACME or type 1.

Have you tried the POL hose yet? I have not yet met a propane tank that accepts the ACME/type 1, but was not also compatible with the POL. Look into the valve on your tank. If it's threaded on the inside then the POL will work. Don't forget: the ACME uses a right-hand thread (rightie-tightie) but the POL uses a left hand thread. In other words POL must be turned in the "loosen" direction to tighten it.