Your coworker needs to bill the company for his continued assistance.
He may not want a side business... But he's already got one, as long as he keeps answering the phone.
He needs to select a consultancy rate which is not inappropriate for the skills and marketplace, e.g. $200/hr
When he gets a call he needs to document who he's talking to, what the problem is, collect the question(s) from the person if brief, otherwise ask them to send an email elucidating all their questions. Don't answer anything and be quick, especially if it's on your company's time.
After he has gone home from the office and is on his own time, he should take on the questions seriously. Perhaps follow up with the person. Then he should "formally write-up" the answer in a sensible, presentable format, and email it to the person.
Then, he looks at the total time spent on it, round up to the nearest increment of time that is not unreasonable, and send a bill to the company for consulting services net 10.*
It is important this not consist of any "new work" but be confined to wrap-up and exit documentation, akin to an exit interview. He cannot be working for two companies in the same field at once. In fact if this goes very far at all, he needs to have a conversation with your current company's HR to resolve any conflict of interest, which there shouldn't be because it should be confined to discussion of work he already did.
If it just gets him paid, awesome.
It may also cause a little excitement, in which case, the next time they call, he says
"Well, I'd love to help you, but the company seems reluctant to pay. Could you provide a PO number ** for this consultation?"
Once he's past the 10 days (or whatever) of the first bill, when they call he immediately steers the conversation to the fact that their payment is late, and he needs to absolutely refuse to give any further help until it's paid. With luck, they'll be so in need of his assistance that they'll expedite payment, in which case, he has a nice little side business.
If they pay... Well, that backfired. He can just keep jacking his rates (with notice of course) until he's soured the milk and weaned them off his aid. In the meantime, free money for what he's already doing...
* "Net 10 days" is a billing term, it means the bill should be paid pretty much as fast as checks can fly in the mail. It is customary in business. Don't use a longer billing term, or they could troll you for that long and collect free support in the meantime, just by being ambiguous about paying you. Other terms are "net 30" or "cash", the latter means you do not trust them to pay, and need to hear some credit card numbers right now.
** "PO number" expands to "Purchase Order number" which means you are asking them to create a Purchase Order for the goods or services. If he gives you a PO #, that's a verbal commitment that the company desires to buy this and will pay. Presumably he will be unable to do this.