Switch email service providers from current host - terminology
I posted this question on webmasters.stackexchange.com but no reply, so I thought I'd try here. I have a feeling it's not appropriate for this site but I'd like some answers :)  

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I've got hosting services provided by FatCow. They use SquirrelMail for their email handler, which has an abysmal frontend, has a low mailbox storage limit, and apparently Fatcow doesn't allow remote access to change a password.

As a result, the webmaster has to change passwords explicitly for the user - ridiculous. Anyway, enough complaining.

What I'd like to do is use the same domain with a different provider, but I don't know the words to begin my search. Provider? Hosting? Client? How do I get started here?

I'd also accept a good recommendation for a provider (or whatever the word is) that solves the above problem description.

Switch email service providers from current host - terminology
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I posted this question on webmasters.stackexchange.com but no reply, so I thought I'd try here. I have a feeling it's not appropriate for this site but I'd like some answers :)  

-----
I've got hosting services provided by FatCow. They use SquirrelMail for their email handler, which has an abysmal frontend, has a low mailbox storage limit, and apparently Fatcow doesn't allow remote access to change a password.

As a result, the webmaster has to change passwords explicitly for the user - ridiculous. Anyway, enough complaining.

What I'd like to do is use the same domain with a different provider, but I don't know the words to begin my search. Provider? Hosting? Client? How do I get started here?

I'd also accept a good recommendation for a provider (or whatever the word is) that solves the above problem description.
