Surely a slight elaboration is required in all this?
In a climbing turn, if the outside (faster) wing literally stalls because it is "at a higher angle of attack", then before it stalled it was generating more lift than the inside wing, and the bank angle would have been increasing, which is not a standard climbing turn.
In practice this well-known over-banking effect is corrected by some up aileron on the outside wing, so the outside wing (as a whole) has a slightly lower AoA than the inside wing, but it is faster so the lift is the same, and the bank angle is stable.
The inner part of the outside wing doesn't get the benefit of this up aileron, and so that is at a high AoA, and so it is just that part of the outside wing which stalls first (theoretically).