How to know if a MacBook battery has been replaced

You can tell if it has been replaced very RECENTLY by looking at the number of charge cycles that battery has accumulated. A new battery will almost always be in the low single digits, i.e., less than 10 cycles, even after verification testing.

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Determine battery cycle count for Mac laptops - Apple Support

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battery runs out quickly

Read If your Mac battery runs out of charge quickly - Apple Support.