The problem is, pop3 mail won't do that, and the iPhone email client isn't designed with pop3 in mind, so you don't get the option of leaving a copy on the server. flyingmember is correct - you're far better off using IMAP. You can set your gmail account to use IMAP, and you might have the option on that pop account of forwarding to your gmail account.
I find it strange because on my last phone which was the Xperia X1 there was a setting which said delete from phone and not server. Not sure if that was because it was Windows based.