I know motive has been questioned here and it's on my mind. Simply "getting a girl" doesn't seem to even begin to cover a crime like this. Reading PP's exhusband's comments about her inexplicable claims of harassment that he claims are unfounded helped me formulate a possible picture.
If she made the claims against her ex in an attempt to convince AP that the ex was still paying her attention, in essence, trying to make him JEALOUS, she may also have been very aware of AP's obsession with MJ. I don't at all believe that MJ was just chosen at random as 'any girl will do'. I think maybe she felt she was losing AP's attention and was desperate to reclaim it. Maybe eliminating MJ was the only way to do it, in her own peebrain.
Maybe she worked AP into a resentful fury at being rejected, had to allow him to sexually assault MJ to get him to kill her, and in her anger, she herself did quite a lot of the damage as far as kicking, beating, and strangling.
I keep thinking about PP's adamant denial in the face of evidence, then AP's fast confession. Maybe AP has the tiniest bit of remorse that PP is incapable of. Maybe PP was the major instigator and AP the follower, so obsessed with MJ in particular that he would take MJ on any terms he could get, even if it cost her her life.
Then again, I have several other theories. Most of all, I wish this had never happened.