Copied/pasted from TSA website:
TSA Pre✓™ Application Process
Available Soon
Current TSA Pre✓™ participants, such as those eligible via a Customs and Border Protection agency Trusted Traveler Program such as Global Entry, do NOT need to apply again via the TSA Pre✓™ application program. They will continue to receive TSA Pre✓™ eligibility.
Citizenship
TSA Pre✓™ applicants must be U.S. citizens, U.S nationals, or Lawful Permanent Residents (LPRs)
My wife has a GE membership, but she has never been able to get Precheck status as the current TSA policy do not allow LPRs (except those who leave TT number off their secure data profile and use frequent flyer status instead) to be eligible. I'm very hopeful that she will be able to go with me going thru the PreCheck lanes. ^ I'm looking forward to the end of the days when we split up at PreCheck and cattle lines and meet at the gate.
