Don't have anything concrete, and just a guess on my part, but maybe this photo was taken after he relieved Field Marshal von Rundstedt on March 10th, 1945 in the west?
I'm not sure. I think it could have been much earlier, as the Assault rifle became standard issue in Autumn 1944. This could be from a shooting trial or something.
But Kesselring had been occupied in Italy before the weapon was "used" in the east, or in a shooting trial. And the man was wounded after his Italian time before he went to the western von Rundstedt command. I simply figured it had to happen after he replaced von Rundstedt. As I said, a guess on my part.
You are probably right, but it looks like the picture could have been taken in Italy where the Germans fought til the end of the war - maybe Kesselring being visiting inspector general or something. I found a link with the picture in it that claims the weapon is an Stg43 not the MP44 which was the final model of the Sturmgewehr ultimately issued starting in late 1944. http://www.geocities.com/pentagon/2833/heer/infantry/mp43stg44/mp43stg44.html