How can I enter the U.S. border with an expired conditional green card?

You will not be able to enter. As a result, it is advisable that you contact the U.S. consulate or embassy in the country where the green card expired to obtain a permit that will allow you to return to the U.S. by filling out a form I-131A, Application for Travel Document (Carrier Documentation).

You will likely have trouble boarding a plane with an expired green card. The required procedure is to apply for an entry document at a U.S. consulate or embassy abroad.

You should be able to get a stamp at a U.S. consulate allowing for re-entry.

You will need to get a travel document from the U.S. consulate.

No, you will not be able to enter on an expired green card or a conditional permanent resident card that is no longer valid. However, you can go to the U.S. embassy and request a temporary travel document.

File a police report where you lost your green card. Go to the embassy or consulate and inform them of the lost green card. The embassy or consulate will stamp your passport so you may enter the U.S. as a legal permanent resident.

Connect with a USCIS transit center in the country where you are located, and they will issue a travel letter. If you are crossing a land border, you can show up and talk to a Customs and Border Protection officer, but do not do this at an airport.

File an I-131A and get a travel letter from the nearest U.S. consular post.