No,she cannot get her work authorization right away

They have to file I-130, after it is approved, she can then file I-485 and the form for work authorization. But it will take more than a year for the I-130 to be approved. And while their case is pending, she need to maintain her legal status by herself before get her GC. It is not a good idea to stay here with an expired visa.

If he is a citizen, then they can file I-130, I-485, and work authorization together. My work authorization took about 100 days to arrive after the USCIS receipt date. I applied my GC after my hu*****and became a citizen, because there was no much benefit to apply while my hu*****and was a GC holder.