Seeking Advice on Venting a Stove in a Townhouse

[Patrick M.]

Greetings all- after 6 months of a well-performing lease on my first deal, I have my second deal under contract! Overall, the inspection shows the place is in pretty good shape with mostly cosmetic fixes.

The inspector did notice that the microwave installed over the stove/range vents not up into what looks like a vent system above the microwave, but out into the room just above the microwave door. He recommended I get someone who can remove the microwave, adjust the vent to go back up, and if need be, build or repair a venting structure to the outside wall about ten feet away. 

This is on the interior wall of a townhome, so the vent needs to run to the rear wall, and then outside. 

Has anyone done anything like this in a townhouse? Any advice? If so, what did it cost? Thanks!