Henry V: "though we seemed dead, we did but sleep"

A connection between 2 Henry IV 4.3 and Henry V 3.6, which I don't recall noticing before.

Starting at 3.6.115:

MONTJOY: You know me by my habit.
KING HARRY: Well then, I know thee. What shall I know of thee?
MONTJOY: My master's mind.
KING HARRY: Unfold it.
MONTJOY: Thus says my King: 'Say thou to Harry of England, though we seemed dead, we did but sleep. Advantage is a better soldier than rashness. [...]'

I'm thinking this might hit Henry rather hard, since he mistook his own sleeping father for dead in 2 Henry IV 4.3. When his father awakens to find himself alone, sans crown, he demands to know why Harry walked off with it.  Harry's initial response, "I never thought to hear you speak again," is not well-received; Henry IV replies "Thy wish was father, Harry, to that thought. / I stay too long by thee, I weary thee." and continues in this vein for another 40+ lines.  Harry kneels and moves his father to reassess the situation with a humble and apparently heart-felt speech.