That depends on the post. Processing times are on www.uscis.gov
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The Work Permit ("Employment Authorization Document") will take about 60-90 days from filing. The I-485 approval may take quite some time. Processing depends on: normal USCIS processing time for turning around the application, and whether the priority date stays current. Normally, if the priority date was to remain current, it would take about 5-9 months--give or take--to process the application. However, as this category is likely to retrogress come October 1st, it may be several years before it opens up again. The good news is that during this time, the beneficiary is generally considered to be here in an authorized status and can renew the Work Permit. Meanwhile, if the petitioner Naturalizes while waiting for the F-2A to be current again, the pending I-485 can be upgraded to immediate relative processing, which would mean the priority date doesn't matter any more and the green card will be issued--barring other inadmissibilities and assuming its done properly--within about 3- 6 months of upgrading.
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Probably years, as the priority dates will retrogress in October.
J Charles Ferrari
Eng & Nishimura
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