You should file Application to Replace Permanent Resident Card (Form I-90) to U.S. Citizenship and Immigration Services if your current green card was partially or completely damaged, lost or stolen.
A copy or your original green card must be also submitted along with Form I-90. You should show some evidence of your identity upon USCIS request, such as copies of employment authorization card or valid external passport. If you turned to police in order to find your green card that was stolen, a copy of the police report should be submitted to USCIS too.
February 2, 2019