I'm afraid there isn't really anything you can do but wait.
Unless you have compassionate circumstances (i.e. a loved one in the US is dying and she must travel urgently), there isn't any way to expedite the application.
As long as she made her ILR application before her BRP expired, her right to work is automatically extended under
Section 3C Leave while the application is processing, so after March 5th, nothing regarding her immigration status or right to work will changes and she can legally continue to work, regardless of whether the ILR has been granted or not.
If her employer wants to check her right to work in the UK, they can do so here (they just need her details and ILR application number):
https://www.gov.uk/employee-immigration-employment-status