This is the way I do it.
It's the only method I've been able to figure out, and there might be a much better way to do it, but it works for me.
1. Edit /etc/cl.selector/php.conf
2. Add these lines right at the top of the file:
Directive = sendmail_path
Default = /usr/sbin/sendmail -t -i
Type = list
Range = /usr/sbin/sendmail -t -i,/bin/true
Comment = Switch to /bin/true to disable php mail
3. In the client's cpanel, change the sendmail path to /bin/true using "Select PHP Version > Switch to PHP Settings"
He will no longer be able to send via php mail