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I have a Surface Pro3 that was approximately destroyed. I managed to rescue the hard drive, but need to connect to it. Is there an adapter that will let me treat it like a regular SATA SSD?

They do not use hard drive. They use solid state drives. They use a mSATA interface. So you will need a mSATA to SATA adapter so you can plug it into a computer. There might be a mSATA to USB adapter for convenience.

I believe what you are looking for is this: https://www.amazon.com/Drive-Adapter-Con