You can make your own from angled stainless steel that would sit as a flange on the new framing between the ceiling joists.

Is this a commercial kitchen it looks like one and if so you will need more than a home hood .

Thank you for the responses! Abbaka no longer exists so, we are not able to contact them. It is not a wall mounted hood. It is an island hood that will be suspended from the ceiling. And no, it is not a commercial kitchen. That's just a pic from the internet of the same hood we have at home.

Abbaka was purchased by Bluestar Cooking who owns the rights to the technology and the name brand. You will see this brand listed under Bluestar’s ventilation products on their website. It might be worth a quick call to Bluestar to see if they might have the part. No guarantees, but “nothing ventured, nothing gained.”

As I recall, Abbaka was purchased by BlueStar, so they may be able to help you.

In any case, it may help to analyze how the parts hang together. In the case of my Wolf Pro Island hood, the chimney section bolts to the framing; the hood bolts to the chimney section. If applicable, you would bolt the upper section to the framing, the middle section to the upper (from inside and below), and then the hood to the middle section. See if there aren't threaded holes for machine screws to do some of this.

Or take yours apart and photo the interfaces for our benefit.