Weapon of Quickening

Dose Weapon of Quickening work like

Cast WQ then all the spells i cast within 13 seconds get the recharge boost or is it like they only get the boost while i have that skill active, So if i cast a spell and it started out with the boost and then Wq ended would it go back to its normal recharge rate?

i am fairly sure that if it had WQ active when you first cast the spell, it would make the recharge quicker even if it ended

The boost is applied to the spells when its cast time is over. It isn't "taken away" from the spell half way through.