other.server.net would be whatever server you are wanting to send out mail through.
Is the other server a cPanel server? That is the assumption that I was working on, but it doesn't have to be the case. The main IP address of your server needs to be able to relay mail through other.server.net. On a cPanel server this can be accomplished by writing a perl script or fetchmail or some other system to log into a valid POP account (it can be a dummy POP account) on other.server.net so that your server's main IP is always listed in the relayhosts file on other.server.net and can always relay mail through it. There may be alternative methods for accomplishing this same task.
If other.server.net is not a cPanel server, then it would depend on what type of relaying model that server provides. If you can configure other.server.net to always allow relaying from your server's main IP address then you wouldn't need the POP-before-SMTP aspect.