As I understand you want to make access to your billing (WHMCS) through the URL like:
whmcs.example.com
Right ?
If so then create the virtual host/account with the domain name/subdomain whmcs.example.com on your other server then edit the DNS zone of example.com on your primary server and add the DNS record like:
Name: whmcs.example.com.
Type: A
Destination: xxx.xxx.xxx.xxx
where xxx.xxx.xxx.xxx is the IP address used by whmcs.example.com on your second server.