There are two easy ways of doing this.
First, you could set up a forward for the root email account. All emails to root will be forwarded.
`echo "email@example.com" > /root/.forward`
OR, Secondly, set up an alias for root as an external email address
echo "root: firstname.lastname@example.org" >> /etc/aliases && newaliases
Beware that you only have one entry for root in the /ect/aliases file