This has always been one of the most nagging questions for me too. And one of my biggest frustrations with Undisclosed.

Looking at the timelines on Serial's website for this window of time during Serial was the first time I really noticed that Adnan was lying right along with Jay. They showed him claiming that he was back at school ~11:30, but then also mentioned that he was late to Psychology class (1:27pm). I was so happy when SK at least mentioned it on the last episodes of Serial:

Adnan has said various things, but not that they went shopping. What seems most likely according to what Adnan told his attorney at the time is that Adnan hung out with Jay until about 12:45-1:00 p.m. and then went back to school.

But I feel like the Undisclosed team has done everything they can to completely gloss over this window of time. In her first appearance on The Docket, SS spent a good deal of time discussing Jay's whereabouts for the 12:07 and 12:41 calls and how the pings didn't match up with Jay's story, but also said that Adnan was back at school by noon (conflicting with what he told his attorney). I asked her for her reasoning or support for this claim but unfortunately didn't get a response. Then on first episode of Undisclosed, entitled "Adnan's Day" they completely jumped from the morning when Adnan gave Stephanie her present to after school, with no discussion of anything in between. And then on "Jay's Day" they talk about Jay's inconsistencies about this time, but Adnan is conspicuously absent from the discussion.

I just wish we had more information because I think that window of time is the key to figuring out if this was premeditated or not. But I imagine if there was an innocent explanation for what they were doing that morning, we would have heard it by now...