I doubt that the remains of a homeless man would have passed the muster, as a British officer, after the autopsy that the Germans would have had performed on him.
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The found body was in NEUTRAL SPAIN (pro-Axis but neutral) and thus the Germans had minimal and short-term access to body & papers. The finding of the body was already reported to the British so a real 'deep dive' was just not possible for German Intelligence on time alone. Add to this that the operation was a coordinated operation with other actions ongoing that made the found evidence look more valid that Greece was more likely than Sicily.