Each Joomla! authorized (e.g. registered) user can access all his/her IMAP email accounts, including GMail, Yahoo, and any other mail server that supports IMAP, from one web page. It support's Bootstrap responsiveness, so it does not matter if you access it from your PC, or smartphone. The rendering is handled by your site's template.
SP Mail Client has all the functionality you would want from an email client, including strong MIME support, contacts, and folder manipulation, plus all Joomla! features.