Ventilation help

Trying to help a buddy set up a room, and got brain locked on the ventilation.
Here's the situation, he has an Ac that has to be vented outside due to heat output. The AC moves more cfm's than his inline fan.

My concern is the filter won't have time to scrub all the air before AC picks it up and exhausts it out window..
Any ideas as to a way i can exhaust the air and be sure it's been scrubbed?
He also has an Ozone gen. that's designed to be mounted in returns so there's another item to play with..

In room AC's suck. I quit using mine for just the reason you state. Sorry this doesn't help, just letting you know you're not alone.

You got that right... lol
I was thinking of ducting AC into big box with the carbon filter inside, then run to fan exhausting out window..
Just not sure if the lower cfm of fan would put too much back pressure on AC and cause probs. Or if the heat from AC exhaust would cause fan to overheat

i was thinking could you build a inch thick or less frame that would fit over fan. line the out side with screen materal and fill the inside with carbon, kinda like a double screen affect but with carbon in the middle