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| || |As far as I am aware, if you are granted a B permit, your wife will also receive a B permit which piggy-backs on yours, and which she can use for work purposes. Though, her potential employer will have to complete some simple paperwork first (though nothing as onerous as what your employer will have to go through, i.e. proving that you were the only suitable applicant for the job after having advertised the role within the EU and Switzerland).
Have a search for some threads in this forum - it has been discussed many times before
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this was my situation (wife is not EU citizen or US citizen) and I concur. US Green card status has no bearing. I am a US citizen though but don't that makes a difference regarding what the B permit allows.
Also, I will warn you, if keeping your US green card is a priority, that you make sure you cover this as well as theoretically keeping a green card requires to live in the US. There are special filings that can be made however.