I liked the answer by @kilisi - simple and to the point.
However I'd go further.
You should report this contact and request by your former manager to your new employers.
The fact that he left on bad terms simply underlines how serious this could be. You may not know the back story and their may be more to this than just your contact.
This is either your manager planning to use your work to his benefit (misrepresenting them as your work) or seeking confidential material for his new employers (how serious this is depends somewhat on specifically what he asked for).
I would advise making an email to the head of HR where you are now explaining what happened.
Advise them that you find the request inappropriate and while you want to either ignore it or turn it down, you feel they ought to know and that you would appreciate formal advice on whether to respond with a rejection or simply ignore the request.
You need to protect yourself from any possible repercussions of what this guy does. He may be contacting other people as well.
It is then up to your employer to decide how they want to handle the matter. They may want to complain to the other company. They (more likely) will do nothing. But you are protected.
I just got an email where he's asking me to send him work documents I prepared years ago, with him as manager, to use at his new place of work.
Keep that email !
Print it out (preferably with the full header information showing) and keep a copy for yourself as well as for your employers.
Keep a copy of the email you send your employer.
Do not do this reporting verbally.
Keep records and keep records of any contact you have with this former manager.
My only hesitation is that I've actually seen former coworkers, at my present office, bring with them & use docs that they prepared while officially employed elsewhere (making me think that the rule of not sharing such materials between workplaces is more honored in the breach.) Even so: they were bringing outside work materials to their current job, not circulating them to former coworkers now employed elsewhere.
This is irrelevant.
What other people do that is inappropriate is not what you should do. Those are choices they made.
Now it's certainly perfectly reasonable that you stay in touch with former colleagues - that's just networking. It's also quite common for people to make use of material they got through previous employment.
What is problematic is that this former manager went out of his way to seek this information longer after he left. And not from a friend, because you were not friends, but from a former subordinate. That's just wrong in so many ways.
Certainly it sets a precedent that I'm willing to do essentially free work for him
This is a very bad notion that I need to address.
You cannot do work, paid or free, for another person without your existing employer's permission (unless you have a very unusual contract).
And supplying internal documents from your current employers to anyone for money would be grounds for instant dismissal and possibly even accusations of industrial espionage. Giving it for free would almost certainly get you fired as well, for a breach of NDA.
Under no circumstances let the idea that being paid creep into your mind as making this reasonable.
If there was any discussion of your former manager paying you for this information it is extremely serious and you must tell this to your current employers.
Once again, you do not know the full story on why this guy left but you know it was on bad terms. Protect yourself.