Did she get her status change from within the US? Sometimes USCIS SAVE database gets updated very late.
Normally SSN office should not deny the request outright unless you did not go with the right set of documentary proof (offer letter, H1 approval notice, I94 etc). Did they give you a denial letter? If they refuse to take her application, ask for a denial letter.
Make sure you go with all documentary proof. Most likely they will take the application and give you a letter saying that you have applied and its pending verification. They would then follow up with USCIS for the status verification. Can take 8 weeks and beyond. But in the meantime, on the basis of the SSA letter, she should be able to work