If the solenoid is physically damaged, you know what is wrong and what needs to be replaced. End of story, and no need for a smoke test.
P0440 - Evaporative Emission Control System Malfunction
This fault code suggests there is an electrical problem with the solenoid or its wiring. That is totally different from a leaking solenoid. The smoke test could verify the valve is leaking, but then the fault code would refer to "small EVAP leak", which is a mechanical problem. This code says you have an electrical problem.
If you are going to pursue this yourself, I rarely approve of throwing random parts at a problem unless testing leads to that, but in this case, consider replacing the solenoid as a test. If it solves the problem, you'll have saved the cost of the diagnosis. If it doesn't, you'll have eliminated one of the things your mechanic needs to check.
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Monday, March 27th, 2017 AT 5:49 PM