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This nozzle extension is apparently from engine F-5034.

Alan Lawrie tells me that engine F-5034 was the spare assigned to S-IC-5, the first stage of Apollo 10. Shortly before the stage was to be shipped from the Michoud Assembly Facility to the Mississippi Test Facility for static firing, engine F-5036 was removed from the stage and replaced with F-5034. Presumably, F-5036's nozzle extension stayed with S-IC-5 and was launched while F-5034's nozzle extension eventually wound up here at Marshall.