The phone is playing a precisely analogous role to the role that the biological memory was playing. So if we say that my biological memories were truly memories—that is, part of the mind—then my phone is likewise storing my memory’s part of my mind: it’s helping me navigate. That is to say, there is no privileged border of the skin and the skull when it comes to the mind. What matters is the role that it plays.
The phone or Google or the Internet can, in principle, play the same role that that biological memory was playing: part of the mind—if not part of consciousness.
If that concept of the self and the person can bring in the unconscious mind and can bring in the body, it can also bring in parts of the environment. So I think one needs to conceive of ourselves as creatures which are not just narrowly limited to some point in Cartesian space, but as creatures that, really, more fully inhabit the world in a more distributive way.