this is my situation:

I have several POP3 accounts around the world. I check these with a Client Mail that download the mails and stores it in a "local space" (harddisk). If I check the mail from my Desktop PC i can't read these with my notebook because the mails doesn't exist anymore on the server.

I would a centralized mail system (so i can read them with desktop pc, notebook, tablet, ect...).

So i think this solution:

Mail Acccount 1 --- POP3 ---
Mail Acccount 2 --- POP3 --- [My IMAP Server, Zimbra?] --- IMAP --- [pc, notebook, tablet, ect...]
Mail Acccount 3 --- POP3 ---
One IMAP Server that stores all my POP3 Accounts...so i can check this IMAP Server with many mail client (notebook, pc, ect...); all sincronized.

Can Zimbra help me?