Switching to Improved Pact Weapon at level 3

Question

My player (Warlock lvl 3. Hexblade, Pact of the Blade) and I are in a discussion about switching Invocations.

He wishes to, now that he's went from level 2 to level 3, switch to 'Improved Pact Weapon'

However, the book specifies:

Additionally, when you gain a level in this class, you can choose one of the invocations you know and replace it with another invocation that you could learn at that level.

The Prerequisite for Improved pact blade is having Pact of the Blade (Which you can only learn at level 3), so if the text is correct, he cannot switch one of his current eldritch invocation to that one, since he couldn't learn it at level 2.

However, his argument is that it's strange that there's no level prerequisite to it if you couldn't learn it then.

Anyone who could help out?

Answer 1

The Warlock can take Improved Pact Weapon

Additionally, when you gain a level in this class, you can choose one of the invocations you know and replace it with another invocation that you could learn at that level.

Jeremy Crawford has clarified:

Q: [I]n the warlock rule for retraining an invocation on level up, what level is "that level"?

A: It's the level you just gained.

So, that means that since the Warlock qualifies for Improved Pact Weapon at their current level (having met the prerequisite of gaining the Pact of the Blade feature), they can replace a previously taken invocation with it.