(And a headcanon for you, too.)
As part of his Stalag 13 operation, Hogan frequently passed himself and his men off as members of professions they did not, and never would, belong to. Usually, this was to complete a mission for the Allies, or some other equally important purpose. But, once in a while, they did it for mundane reasons, or just to see what they could get away with.
One of these instances was Thanksgiving. Only the Americans observed the date, but any excuse for LeBeau to make a gourmet dinner was a good enough excuse, so the task fell to Hogan to smuggle a whole turkey into camp. Small items could be brought in by Schultz, but an entire live turkey was too much to ask for.
Hogan had a plan, though. He sold Klink on the notion that he had been a skilled ornithologist back in America, and wove stories of ruby-throated warblers, river finches, and other such nonexistent species that he'd supposedly personally identified. Soon enough, he got Klink convinced that there was a band of rare wild turkeys roaming around in the woods outside of camp, and that a fortune could be made in the birding world if one or several of them could be just captured and identified.
One live turkey went into camp, courtesy of Hogan's scheming and Schultz's occasional assistance, and none went back out. Klink wasn't keeping very close track, anyway, and it was easy to say they'd just let the bird go free and it'd flapped and squawked away on its own. Hogan promptly dispelled the situation by explaining that the turkey wasn't part of the endangered species he'd believed it to be, since the distinguishing characteristics weren't prominent enough to be seen from a distance, and that it was a common mistake that happened all the time, et cetera.
And so, Klink may have been left without a prize turkey at Stalag 13 (Hogan later joked that Klink was the prize turkey) but the men got their Thanksgiving dinner.
(Inspired by this picture.)