You could also do something a little more personal, maybe reach out to other sisters (facebook, even here on GC) and see if any of them would be willing to write her a little note or send her a card congratulating her on her initiation into XYZ.
I did this for a collegian (I had been her high school cheer coach) and to this day she remembers how special my letter was.

I'm glad she was accepted and to be honest, unless the person was a criminal and not a good person WHY would any FHQ turn down a new member of their organization? Maybe it was harder in the past, but it is not in a sorority's best interest to turn away someone that wants to be part of their organization!

Has your friend been initiated? Can you come back and tell us what GLO now?

This!