If you both have the exact same elements the edit should open up totally normal. Where I work we constantly give each other just the prproj file because we all have exactly the same editing elements, such as promos, lower-thirds, bumps, voiceovers, music, animations. So basically it's extremely simply because we have a folder structure for each program that we edit and that makes things extremely simple. So at the very most we have to relink 4-5 folders because once you re-link one thing a category/folder everything else is auto-pilot. Because Premiere then finds the rest of the stuff from that specific category inside the folder. So re-linking is fairly easy, as long as everyone keeps their folders correct.
However like Steven correctly mentioned you can go to project>project mananger and you copy all your clips to a new folder/location. You can make it create a trimmed version of the project or a full version of the project. But if you and the other person both have the exact same stuff then you shouldn't need to even use the project mananger, if you re-link all the media correctly there shouldn't have been any issue, I've done this literally 1,000 times and never had a problem unless I accidently mis-linked something.
