-See the following at:
https://help.cbp.gov/app/answers/detail/a_id/75/kw/lost%20green%20card%20while%20abroad/suggested/1
If your I-551 is stolen while outside the U.S.; please notify the police department in the jurisdiction in which your card was stolen to obtain a police report and contact your nearest U.S. Embassy or Consulate to request a U.S. Government Transportation Letter or Boarding Foil. Please be aware that you may be required to complete the I-90 form: Application to Replace Permanent Resident and paying the fee at the time of your re-entry to the U.S.
Read this website for how to apply for the Transportation Letter in Guangzhou or in Beijing (depends on where your child lives in China-which location is convenient to her):
http://guangzhou.usembassy-china.org.cn/lost_and_stolen_green_cards.htmm/
Note: The Transportation Letter is needed for boarding the airplane.
我是母親,現在在美國,可能能找到她的綠卡掃描件。
-Email it to her, and then, she can print it out in a color printer for Transportation Letter application.
謝謝!