Well you have to identify why a java program javaw.exe is trying to connect to the internet using an email port. The occasions on this forum have related to the Azureus P2P program, used for file swapping (Peer 2 Peer, e.g. PC 2 PC or user 2 user). There may be other java based P2P (file swapping, music downloader, etc.) programs that would use this file, but right know I don't know of any.
I assume that the URL in the image you posted relates to your ISP, if so it looks similar to other occurrences.
You could check in your firewall logs to see if there is any way to check what program launched javaw.exe, or you could try a program called process explorer from sysinternals.com.
I wouldn't recommend terminating the internet mail provider as it may be the first indication that you have malware using your system to either send span or connect to the internet using the email ports, possibly to avoid detection.