You are right, I think it is a 359. I am assuming, as you say, that "ac" is Walther made, and "44" is the year of production. Are the inside of the grips supposed to be serial numbered? I can't find any serial numbers on the grips. I was just notified, my 1943 holster, and two WW2 vintage mags are waiting in my post office box!
I have always wanted a P38 since 1965 I was 13 or so, and saw one in Small Arms of the World. It was cemented by the fact that Napoleon Solo (The Man from UNCLE) had a P38K. The Luger never caught my fancy, and though I dabbled with Broomhandles in the 80s, I have always wanted a wartime P38! I have had opportunities for P1s when they were cheap, and even a Grey Ghost 1946. Never struck a chord, though. When my friend offered me this, I was besides myself. It is perfect to go with my S&W Victory Model and my Inland M1carbine.