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Scipio....can you tell by the photo of the phone in the kitchen of WHF as to whether the cream round dial phone was lacking the integral cord? I'm hopeless at this!
The only way to tell is to see the back of the phone. I can say with great confidence that police had no reason to turn the phone around in order to take a photo of the back.
I can also fairly confident that even if the bedroom phone was the new one without an integral cord that Jeremy would take the cord and phone not just a phone with no cord to the kitchen. Only if he knew there was a cord already in the kitchen to use would he have the ability to leave the bedroom cord. The housekeeper and secretary said the kitchen phone had the cord wrapped around it when it was found. That leaves only the cord from the cordless phone cradle as a possibility and I think Pike would have made sure he collected the cord when he retrieved the cordless phone. He mentioned making sure he took the splitter adapter which allowed 2 phones to be used in 1 socket.
So all in all I doubt there was a phone cord sitting in the bedroom.