There any way to sync the emails from our customers to the outlook, as the vast majority of companies that contract calls this function sync both calendar and notes with outlook. You may give him a bit of importance to the issue?
You can setup Outlook to use IMAP so that email is stored on the server. This will ensure the email you see in Outlook is the same as you will see in a webmail application like Roundcube. As for calendars and contacts, you would have to check with Outlook to see if there is any support for syncing items from a specific webmail application (e.g. Horde, Roundcube).