1. Download the latest firmware:
http://dus01.ps4.update.playstation.net/update/ps4/image/2016_1011/rec_741cfe2f0dec1bb4663571de78ae31cf/PS4UPDATE.PUP to a USB stick. Place the file in the update folder you make by following these steps
2. Swap out your drive with the Pro's drive
3. Plug in the USB stick with the firmware on it and boot the PS4 into safe mode by holding the power button until you hear two beeps. Make sure you do this with the console fully shut down (no rest mode).
4. Plug a controller in via USB like the screen suggests and press the home button to sync it to the PS4.
5. Select "Initialize PS4 (Reinstall System Software)" and go through the steps
6. After the OS is installed and you can use the PS4, go into system and restore your PS4 with the backup you made.