Setting up Remote Email
This is now quite easy in Cpanel as they made changes that work well.
You only need to go to MX record and set the IP or domain name of your remote email server there. You can also setup a secondary service which can be the local mail server but you need to set it as the mx Priority as a higher number.
So you would have lets say a mail service named cs1.hvmail.net and they may have one called cs5.hvmail.net
You can set mx 0 to cs1.hvmail.net
mx 10 would be set to cs5.hvmail.net
The local would be mx 20 where local is your domain name
Nothing too much to it.