Hello Anonymous from Georgia,
It would be faster to obtain your spouse's green card if you became a U.S citizen. However, it is important to see if your spouse is able to file for this in the U.S. before you start the process. Some things you would need to ask yourself are 1) Did he/she enter the U.S. lawfully? That is, they were inspected by an Immigration officer at the border, etc., and you should have proof of this.
You should consult with an immigration attorney to discuss your specific case in detail especially if your spouse did not enter legally, or has criminal convictions, before you start the process.
Good luck
Notes: This information is of a general nature and is not, nor is it intended to be, legal advice. You should consult an attorney for advice regarding your individual situation.
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