Q: how to transfer contacts and message history from samsung note 3 to iphone 6 plus

No way that I know of to transfer message history, but contacts could be transferred with your Gmail account. Guessing that you have your contacts in Gmail for the Android device. Another option is to transfer the contacts to the computer to a supported application for the iPhone, then sync them to the iPhone.

You can visit : Move content from your Android phone to iPhone

From this Apple Support website, you can get information about how to transfer contacts, music, photos, videos,  documents, and more from your Android phone to iPhone. But for text messages, you may need other tool.

Cool! I never knew (or had long since forgotten about that link). Good stuff.

To move messages and contacts from your Samsung note 3 to an iPhone, you need to follow the guide: Move content from your Android phone to iPhone - Apple Support

I think the new Mac OS X Yosemite already has a native way to back up (if not show) the text messages from the iphone. For Windows, I use copytrans contacts as a simpler way to back up texts: http://www.copytrans.net/suppo... The bottom line: it works but there is no way to restore them back to another phone without having to use iCloud backup/restore.