A good rule to follow in the US is that if you have to do anything legal, be prepared to show your social security card or birth certificate.
And I've known a few South Americans that were living as citizens in the US but had to show a birth certificate upon getting divorced. It had something to do with changing behind-the-scenes paperwork about their status. If she is the one filing, that could be why she's asking and not him - to provide it to her lawyer.
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