We know that Yui was saved in Kirito's NervGear's local memory in the first season of Sword Art Online but in in the second season when Kirito is in Gun Gale Online, when everyone is watching Battle of Bullets Yui is there with everyone else watching it in ALO. she also talks to Asuna on her phone when she heads off to the hospital and in Agil's bar when Kirito sets up the cameras for her.
in all of these cases Kirito isn't using his NervGear and i would suspect it is turned off. so where is Yui now stored? and how is she able to go from this place to ALO, Asuna's Mobile and the cameras in Agil's bar?