That's got me baffle too I had thought it was the same woman that Miles at when to and the pictures on the walls were of Walt and maybe Micheal when he was younger. And maybe Miles visit was during the time Walt and Micheal were on the island. And after Miles tells her everything is okay now she moves to New York. Micheal find her there and take Walt to her and they can't say anything about where or what has happen to them in fear of Ben.
So when Micheal was passing Miles going on to the freighter Miles picks up vibes from Micheal and knows he's not who he says he is etc as what was shown on the show.
Ben knows that Walt is in New York remember him telling Micheal over the call from the mainland on the freighter.

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Standing in the ocean with the sun burning low in the west
Like a fire in the cavernous darkness at the heart of the beast
With my beliefs and possessions, stopped at the frontier in my chest
At the edge of my country, my back to the sea, looking east