If it uses the same data logger as the VP2, I have one you can have, when I replaced my 2002 VP2 with a new one in 2015, the old data logger was no longer compatible as the new VP2 had the latest V3.x firmware which wouldn't recognise the original unit. It's currently "stored" in the old redundant VP2 console.
I've just had a look on the Davis site and it appears the data logger for the Weather Wizzard III is considerably different to the VP2 unit. It appears to be an external fairly large box which connects to a socket on the WW3 and then connects to that Davis A.T 9 pin adapter. The VP2 one is a small 30mmx20mmx10mm approx unit with 20 pin socket on it which fits in the back of the VP2 console.