Theory: he found out about her since the beginning of episode 4 but finding her ID confirmed his suspicions. Or finding her ID made him think about the past clues and putting them together.
Minwoo should just appreciate his girlfriend or just break up with her again…his face showed jealously when Hari told him that she went to the concert with a man.
https://youtu.be/tkmJrwRW9W4
https://twitter.com/cleanxbee/status/1501833364495794180?s=21
https://youtu.be/G72rSMNq7po