... One wonders if Murphy made herself vulnerable to be taken by Odin when she spent so much time
training with the Einherjaar. After she left the police force she was adrift. After Harry seemingly died I think she also became disillusioned about her faith, she seemed to have found a purpose when she started doing some work with Odin. If she hadn't been dismissed from the police force and had remained a practicing Catholic I doubt she would have woken up in Valhalla.
I think this is part of Uriel and/or Odin pulling another fast one.
As part of Uriel's "spook squad" (running under her dad's office), she gets to work directly against the plans of the Fallen, in realtime/now, without waiting for the Einherjar "beyond living memory" to kick in.
But as one of Odin's soldiers... well, as it happens, she gets that shiny new Einherjar body.
Odin and Uriel roll their eyes helplessly and go "Mortals, sheesh... wotcha gonna do?"
(ya gotta use your imagination to see the wink&nod passing between them... but it's there)