By a Bishop. In the way I had drawn it, the orthogonal moves you describe would not enter a4' directly; they would enter a4, and then optionally transfer to a4'.
The other phrase you quote was intended to describe what happens when you start on a4/a4'.
It is still a bit ambiguous how a knight could move from h6 if h5/h5' is occupied, (and the switch thus in a known position).
By a Bishop. In the way I had drawn it, the orthogonal moves you describe would not enter a4' directly; they would enter a4, and then optionally transfer to a4'.
The other phrase you quote was intended to describe what happens when you start on a4/a4'.
It is still a bit ambiguous how a knight could move from h6 if h5/h5' is occupied, (and the switch thus in a known position).