The link you supplied actually does say that the person with a work eligible social security number will get the credit. Therefore, since her SSN is not valid for work, she is not eligible for the Stimulus payment unless you are active duty military.
"How are married couples affected, if only one spouse has a Social Security number?
As with EIP2, joint filers where only one spouse has a Social Security number (SSN) will normally get the third payment. This means that these families will now get a payment covering any family member who has a work-eligible SSN.
For taxpayers who file jointly with their spouse and only one individual has a valid SSN, the spouse with a valid SSN will receive up to a $1,400 third payment and up to $1,400 for each qualifying dependent claimed on the 2020 tax return." Work Eligible Stimulus SSN
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