Manage office emails

I am a regular user of e-mail, but would like to change things in the office here, and I need some information.
There is a way to access all office e-mails, centralized so that I can refer to them when I need?
Today, I have to look for old emails in each office computer, and it takes a long time.
There is a way to do this without setting up a local e-mail server and still use DreamHost?