domain, website different servers and A Record!

First, let me start by apologising, I am brand new to cPanel and my question may reflect that! I have a "coming soon" website which is located on my existing server, where mail and a lot of downloadable technical content (pdf files) also is hosted. The actual "production" website is being produced by an advertising company with their own web department, who demand that the website itself is to be located on their server if they are to maintain this - which they are. If they are also to host all the technical downloadable content and the mail server, the price will be enormous, so they have suggested that I point the A record to their server (e.g. ip address 12.345.678.90), and I keep the domain (e.g.