It still seems so odd to me that originally Elaine said his last text was sent at 8 PM. I would think she had his cell log from her phone company or could see it online.
So why didn't she see the 9:37 pm text at that time? Or did she, but never mentioned it for some reason?
I still don't think DR texted an outgoing message after 8ish PM. His phone may have received a text, or pinged a tower, but I don't believe he texted anyone past 8PM. "electronic communication" is extremely vague and can be simply the phone and it's cell signal making a communication. I think it means the phone no longer registered anywhere after 9:37PM.
and I believe that means MR had the phone between 8-9:30 and disposed of it at 9:37 or soon after. I think that's why the info about that "communication" came out later - to let MR know that they tracked the phone for over an hour after DR's last texts stopped suddenly. I think it was meant to push MR's hand. and that they could track the phone's location and MR's location to prove he and the phone were in the same place.