The ONLY way I would pay a judgment that old is through an attorney who represents the plaintiff.
I would not respond to the letter. Instead, I would wait 2+ months to see if they renew the judgment.
Check your state law on judgment renewal. Some are unusual, and allow renewal even after the judgment expires.
If the judgment expires and cannot be renewed, I would pay no one a dime.
If the judgment is renewed, or can be renewed in your state after it expires, I would contact the attorney who originally handled the case for the plaintiff. I would never, ever pay a debt this old based on nothing more than a letter.