Greta writes, "I am a permanent resident and last month I noticed that I could not locate my green card. I immediately applied for a replacement card and have received USCIS Form I-797 in response to my filing of USCIS Form I-90. Now, I have to take a quick business trip to deal with an emergency at one of my company's offshore locations. How can I travel?"
You have done the right things so far because a green card holder should not leave the United States without evidence of being a permanent resident (while you will not have any difficulty entering the US because your information is in the CBP database that the agent can access using your passport) because you will not be allowed to board a plane at the overseas airport without valid proof of being allowed to enter the US. What you need to do is to make an INFOPASS appointment, bring along your USCIS Form I-797, passport, and green card file (hopefully, nothing will be needed because all the information will be there for the officer to check but it does not hurt to have all your documentation with you) to request the officer to put a stamp in your passport. When you travel, you should travel with your passport, USCIS Form I-797, and yet again as a precaution, your green card file so that you can reenter without any issues.