Many of you who already have submitted your visa documents ask the same questions when you look for another job within Korea "Do I have to do this all again?" Luckily the answer is "No" however you still supposed to provide an authenticated photocopy of those documents to your new employer. Here are ways of how to prepare such documents.
1. If you are hired directly from the individual employer who went through the immigration process (E2-1), as you have already submitted your documents to apply for your E2 visa, the immigration office keeps a copy of them on their database. you can officially ask to release those documents by visiting a local office. They will release photocopy of your Criminal background check and a Degree with this official cover page called "Immediate Disclosure" (즉시공개서)
You can provide these documents to your new employer instead of providing a new version of the documents!
2. If you are hired by Superintendent of Ministry office of Education through EPIK, SMOE or other public school programs (E2-2), There are possibilities that the local immigration office does not have your criminal background check and a Degree certificate. In this case, you can ask the local office of Education to release your documents.
like you can see the attached Sample, they will put a red stamp called "original verification"(원본대조필) on the photocopy of your documents
3. If you may have to redo your Criminal background check while you are in Korea, please check out this article on the link below, it will tell you how to apply US criminal background check in South Korea.