USCIS has published Form I-131A, Application for Travel Document (Carrier Documentation), a new form that allows lawful permanent residents (LPRs) to apply for a travel document (carrier documentation) if they:

Are returning from temporary overseas travel of less than one year, and their Green Card has been
lost, stolen or destroyed, or
Are returning from temporary overseas travel of less than two years, and their Reentry Permit has been lost, stolen or destroyed.
The length of the absence will be measured from the time the LPR departed the U.S. to the time he or she
pays the Form I-131A fee.

Applying for Carrier Documentation
To file Form I-131A, LPRs must pay the required fee online and then apply in person at a U.S. Embassy or Consulate.

The embassy or consulate will generally issue the carrier documentation within two weeks. The LPR should present the carrier documentation, which may be a boarding foil (similar to a visa) or
transportation letter, to a transportation carrier instead of their Green Card or Reentry Permit. The carrier documentation allows an LPR to prove to a transportation carrier only that they are authorized to travel to a United States port of entry to apply for admission to the United States. It is not a guarantee of admission or parole into the United States. CBP will conduct all required inspections when the LPR arrives at a United States port of entry and will make the final determination of whether to admit or parole the LPR to the United States.