"Whenever a move passes through a4 from below, it can be continued normally, or like the upper board half was not shifted."
That is correct!
"a4' cannot be reached from below."
Of course, a4' (I'll call it 4) can be reached from below. For example, if you start from d1, you can reach the switch 4/a4 upwards. The player must then decide whether to occupy square 4 or square a4 and mark this clearly through his positioning. After that he either stands on 4 or on a4. Then the player can proceed as described in the reply to Fergus Duniho.
"Whenever a move passes through a4 from below, it can be continued normally, or like the upper board half was not shifted."
That is correct!
"a4' cannot be reached from below."
Of course, a4' (I'll call it 4) can be reached from below. For example, if you start from d1, you can reach the switch 4/a4 upwards. The player must then decide whether to occupy square 4 or square a4 and mark this clearly through his positioning. After that he either stands on 4 or on a4. Then the player can proceed as described in the reply to Fergus Duniho.