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Turkey's Sabah newspaper first reported the story saying the audio was recorded on the watch but then discovered on Khashoggi's iphone -- that his finance was holding outside the walls of the embassy.
It has been noted that the LTE feature in Apple Watch 4 is not supported by any carriers in Turkey.
AppleInsider has the most uptodate coverage I could find in print:
https://appleinsider.com/articles/18/10/12/saudi-journalist-used-apple-watch-to-record-own-interrogation-and-execution-report-says