If you have shoplifting on your record will it show up on a background check?

If you were arrested and charged with the offense, and it occurred after your 18th birthday, it will show up.

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but this was over 20 years ago

Added: Sorry to have to tell you that your criminal history record is a permanent record that does not "go away" after the passage of time.

In the UK this is correct and you would not be allowed into the USA and more countries are also taking this on