I'd have thought that would entirely depend the terms of his lender so the easiest way to establish the options would be for him to make an appointment to discuss it with them.
If they do accept adding another party to the mortgage it would be subject to the relevant credit checks as remortgaging so best to get together 6 months payslips, paper bank statements and any required types of ID as you'll likely need it, and will need to involve a solicitor to change any title deeds and ensure all parties agree on type of ownership, any potential transfer of equity and the provision of it should the property be later sold. Most lenders will require this is as standard. There will be a (relatively) small fee to change any title deeds but this is relative to the property price so not easy to advise on without knowing that.
I would also be having frank discussions about % of ownership and how you wish to divide that and strongly consider a deed of trust in the interests of protecting finances fairly. If my partner were moving into my property, however much I loved them I would want my prior equity and investment protected should it end acrimoniously. Equally should you be using any of the funds from the sale of your home towards the improvement of the property, the same stands.
As you say the other option would be to remortgage, in which case the new deal would reflect what was being offered or what a mortgage broker could offer, should you use one so may not be at as beneficial a rate, but equally two people applying for a mortgage will have a preferential deal to a single buyer (finances dependent) as it is a safer bet for the bank.
The first step would be for him to call his lender and ask the questions, and then make an appointment to see what they require and what is on offer, and what (if any) fees there are to extract himself from his fixed rate should he need to.