2001 V6 Ranger should have Type E PATS so no separate PATS module, PATS is in the PCM
PATS = passive anti-theft system, PATS makes the theft light flash
A PATS key has an RFID tag in the handle, each tag has unique number, when you turn on the key in the ignition, the PATS reads that keys tag number
Your original PCM was programmed with 3 PATS keys at the factory, if the key used matches one of these numbers in PCM memory then the starter motor, fuel pump and fuel injectors will work, if it doesn't then these 3 things won't work
The other PCM was programmed with 3 PATS keys as well, can you get one of those keys?
If not you will need to tow the truck to a locksmith that has laptop with Ford software and he can add your PATS key number(s) to new PCM
Or get Mobile locksmith with laptop and software to come to you and add the PATS keys.
PCM can only get keys added while IN the truck and connected, you can't add keys to PCM while it is out of a vehicle
i.e. you can't just take PCM in to have keys added
adsm08 is right you could get the truck towed to Ford Dealer and they can add the keys and change VIN to match