My boyfriend will enter Zurich airport from the US (fully vaccinated)and transit to Sweden. We have to make sure the border control take place in Zurich and NOT Sweden since americans are not allowed in directly from the US, but they are allowed to enter from another EU/EES/Schengen country (stupid, I know). I have talked to the Swedish police and their answer is that we have to make sure the border control take place in Zurich and then we are good to go, so I have to make sure this is the case. Thanks for your help!
The flight from Zurich to Sweden is an "internal" Schengen flight, so basically like a domestic flight in the US.
As such it is impossible to reach that flight without entering the Schengen zone, so you will go through passport control in Zurich. There is nothing special you need to do. Just follow the signs.
US flights arrive in Terminal E and Schengen flights typically leave from Terminal A. Your boyfriend will have to clear immigration to get from E to A.
In the highly unlikely case that he doesn't clear immigrations between the terminals, he can just follow the signs to "exit" and walk out the airside area. Than he has legally entered Switzerland.
Tip: if your boyfriend as lounge access, stay in Terminal E for the layover. The lounge there is much nicer than the one in Terminal A.
Tip: if you have extra time it's easy to get from the airport into town. Local train S16 goes directly from the airport to Bahnhof Stadelhofen (right next to the opera house and the lake). The train ride takes 16 minutes and the train goes every 30 minutes.
Switzerland is member of the Schengen Area so border control will happen on the way to the gate with the flight to Sweden. The flight to Sweden can be considered a domestic flight in this sense.
(Switzerland is not a member of the EU which might have confused the police. A flight via for example Ireland would be much worse. They are in the EU but not in Schengen so it might be possible to just do a transit without border control)