Seems like something that should just be put into the FAQ for clarity.

The argument is if The inquisitor can use focus tokens when shooting jax from range 2-3. The attack counts as range 1 however the ship isn't actually at range 1. My assumption is yes he can.

This doesn't really need a FAQ entry. The wording as stated on the cards is pretty clear. Carnor Jax - "Enemy ships AT Range 1" can't use focus/evade. The Inquisitor - "... TREAT the range of the attack as Range 1." The Inquisitor TREATS the range as Range 1, Jax affects ships AT Range 1. The Inquisitor at Range 2 or 3 can still use Focus and Evade, and also gains the additional die for treating Range 2 or 3 as Range 1.

The Inquisitor's ability specifies that "the range of the attack" is what is treated as range one. Ranges for abilities are checked independently of determining range for the attack. It's quite possible to have a ship that is taking a range two shot at Carnor to still be at range one when measuring from him.

Jax affects ships at Range 1 of himself. Is the Inquisitor at Range 1? No. Therefore, Jax has no effect.