Your customer is a non resident alien with an SSN; she needs to execute a W-8BEN that includes that SSN. It is appropriate to use the SSN rather than the ITIN for information reporting on a 1042S. Her future plans to become a resident alien (not permanent resident) have no bearing on your requirements.
An NRA with permission to work in the U.S. can get an SSN. When or if they become a resident alien is not a direct result of that process.
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.