Edit DNS zone from SSH from /var/named/domainame.db and copy the line with existing MX entry and paste it just below the existing one. Edit that line and set priority 20 for it and the default that your customer wants to be should be set to be 10 or less than that. It will show you 0 right now and you can leave it as it is.
Technically, the MX weights do not need to be different. Two records with the same weight will be load-balanced. Ensure that your customer doesn't want to start load-balancing his inbound mail. Unless your a big shop running multiple in-bound servers, this usually isn't the case.
As a side note, one of the newer anti spam-technologies is "Reverse MX." In an nutshell, all mail should originate from a system that's listed as a mail exchanger for a given domain, and that mail exchanger needs valid forward and reverse entries - they must match. Meaning no CNAME records. In practice, Sender-ID is more likely to go places, but RMX is worthy of mention.
umm after that i have add a second mx i can't receive anymore the emails:
SMTP error from remote mail server after RCPT TO:<[email protected]>:
host domain.com [ip]: 550-host.server.com[serverip] is currently not permitted to relay
550-through this server. Perhaps you have not logged into the pop/imap server
550-in the last 30 minutes or do not have SMTP Authentication turned on in your
550 email client.