How can I know my replace motherboard is original.

You can't really know for certain.

Apple menu -> About This Mac should reveal the serial number.

The Serial number should verify on http://checkcoverage.apple.com/

If it doesn't then it isn't original. If it does, they either have updated the serial number on their internal database, or are using the original.

I've seen both happen to people. I was trained at an AASP, and we are supposed to update Apple's internal database. The proof though exists in reports on Apple Support Communities that occasionally that step is missed.

If it was done by Apple or an Authorized Apple Service center then they would use original parts. If it was not done there, then the parts used would not be supplied to them by Apple and the warranty on the parts would not be honored by Apple.

You can run the Hardware Test, but not sure if it will report the validity of the motherboard.

Use Apple Diagnostics to test your Mac - Apple Support

Are "replaced" and "original" not mutually exclusive?