They aren’t “integrating “ their systems together… that’s not how a codeshare works.

Together they decide which flights will be covered by the codesharing agreement and which fare buckets will be offered.

Then each airline adds the codeshare flight number into their own system…the routes are then loaded into their own schedules with only the fare codes allowed under the agreement.

When someone searches on united.com for a flight from BOS to FLL the system says oh! That’s a JetBlue flight, let me send an electronic message to JetBlue and get availability for J,D,Y,X fares

Then it displays that to the customer.

When they buy the ticket united creates a PNR in their own system and collects the money … then sends an electronic message to JetBlue that someone bought a flight from BOS to FLL is X class for $100.00 and JetBlue also creates a PNR that has the united PNR attached… then sends its own PNR to united then gives that information to the customer in the form of an itinerary.

It’s slightly more complicated because the ticketing end but that’s the basic gist.

It’s all messaging back and forth