I have had my FEO visit and he was happy with everything and I should have my certificate a week tomorrow

Now I have seen a rifle I want but it is being sold privately. Is the procedure the same as buying from a dealer. E.G they fill in relevant details in the available slot on my Cert and a transfer letter detailing their details, my details and the rifle details. Apart from seeing their certificate to check identity and legality to own said rifle is there anything else I should be doing?
Thanks
Matt