An intern who you know will only be there for 3 months is not worth as much as a full-time employee.
The value of an employee isn't just the work that they complete in a particular time period. It's also the anticipation that they will continue to learn and grow and add more value to the company over time. Personally, my second 3 months with the company produced a ton more value than my first 3 months, and my most recent 3 months was a lot more valuable than either of them. That's because I've learned a ton about the job since I started, and because I've also learned a lot about the company and how to work here.
Even if an intern produced the same amount of work in 3 months as a full time employee would have, they still aren't as valuable to the company as a full-time employee who will continue to learn and grow from there.
Also, companies can invest in a full-time employee through stuff like training, tuition reimbursement, and conference attendance.
Full-time employees may be able to access sensitive data or make certain decisions that an intern couldn't.
A full-time employee will (hopefully) still be around after 3 months to answer questions. (I have colleagues who routinely field questions about projects that they worked on years ago; if an intern had done that project, that knowledge would be lost to the organization).
Finally, a full-time employee could potentially be promoted over time.
With that said:
Now he is negotiating that he should be compensated a higher salary since he is not getting to learn anything new but he is going to do the same job he has done before at a different firm. Is this behavior professional and should HR offer a higher salary to the candidate?
The fact that he won’t be learning anything new isn’t relevant in the least - the only relevance to how much you offer him is how much value he can provide to the firm which is, as I just pointed out, significantly less than what a long-term full-time employee would provide. The fact that he has relevant experience already probably is relevant, though. That being said, his value to the company is probably somewhere between what a less experienced intern would offer and what a full time employee would offer.