If you want to know if the recirculation door is working after they replace it turn the auto climate control off, set the vent positions to the blow out of the dash and turn the blower on high. Now turn the recirculation either on or off depending on where you started from, after a few seconds you should hear the sound of the air change and should feel a difference in the force of air coming out of the vents.
This is a major component of the HVAC system so the dealer should never tell you that this is not a big deal.
Part 18B259 is the air inlet duct assembly and inside of that assembly is the recirculation door. Part 19E616B is the actuator that drives the door. The door does not come out unless something is broken and you can not repair it in the car. The door is serviced in the assembly and is not available separately.
For a Ford tech who has done these it can easily be done in a day but I wouldn't rush them. I believe it calls for 8 hours of labor.
This door, or some part of the system that the door attaches to, can become broken due to actuator exerting too much force on the door and stressing the components. It's not an uncommon failure.
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