Maybe because when sunset shimmer saw her reflection into the mirror, she saw her vision of becoming a demon possessing the power of the element of magic, she's studying when she's still celestia's pupil and like twilight she in fact this lead to discover the elements of harmony and this may be the key why sunset shimmer knew what the crown look like,and when the portal open, she was surprised and didn't know that she's in the crystal empire and tried to open every door in the castle and yet she found what she's looking its the crown that possess a powerful magic
Sunset shimmer knew twilight's crown it's because when she saw her self into the mirror ,she saw her vision on becoming a demon wearing a crown and possessing a powerful magic ,when she was still a pupil of celestia, just like twilight she discovered the elements of harmony and it's power and she was amaze,and the time after that sunset shimmer abandoned her study with twilight and by the time sunset return back to equestria she's ready to get it but she saw an image of twilight sparkle of having the crown and she seek for it, finally she saw the crown and by any chance she replaced with a fake crown, so by the time they noticed, it will too late for them to get it from sunset shimmer.