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I have multiple emails using several providers. Gmail, Yahoo, Comcast, Exchange, etc. The things is that almost every email provider today has a web based email client. If you want to use an email client on your desktop, you simply configure the settings to leave a copy on the server, and all your emails will remain on the server, where you can access them from the web from anywhere. This also allows you to access your dowloaded (synced) emails when away from the interent. I would try that, and if the client you have on your desktop doesn't support it, I would use a different one. I do know that Thunderbird (free) has this feature, as well as Evolution (free), and Outlook (never free).
