Reference: [1]
Backup MX
Setting up Postfix to function as a Backup MX is rather easy (assuming you already have it configured to function as a Primary MX)
You need only add the domain you want to buffer mail for to $relay_domains
relay_domains = $mydestination, domain_to_backup.com
Primary MX
Again assuming Postfix is already setup to finction as a Primary MX there are no additional modifications needed to receive mail from the Backup MX.
DNS MX Records
For the Backup MX to function your DNS must be setup correctly. DNS Configuration is beyond the scope of this article, but essentially you need to add an MX record to your DNS server for the Backup MX.
Example MX Record
example.com. 86400 IN MX 10 mx1.example.com. example.com. 86400 IN MX 20 mx2.example.com.
Where mx1 is the Primary and mx2 is the Backup
The number 10 and 20 correspond to the MX's Priority
The number 86400 is the Time to Live value (86400 seconds = 1 day