Here's where I get my mail, just a short hop over Gates Pass by stagecoach--preferably with Andy Devine at the reins while being chased by mounted Apaches.
More to the historical point, this is a linen postcard from the early 1940s showing a portion of the set for the film Arizona (1940) with a sparky Jean Arthur and a very young William Holden. As most of you know, this was the beginning of Old Tucson as we know it today. If the ocotillo in the photo was actually blooming, it might have been taken in the late spring--perhaps spring of 1940, when the film crew returned after a winter hiatus to wrap the movie (see Images of Old Tucson: Western Feature Filmmaking in the Desert, a charming personal memoir by Michael J. Bifulco for more details).
Old Tucson historian P.J. Lawton, author of Old Tucson Studios (in the Images of America series), says that the "post office" was a promotional stunt created for the release of the movie. The film premiered in Tucson at a midnight showing at the State Theatre on Congress (near the Fox Theatre, but now demolished). The only other photo that I have seen of the post office is in Bifulco's book, in his chapter on the filming of Arizona.
For a while, you could actually get a letter postmarked from Old Tucson; later this week I'll post an example.