It not possible out of the box to copy emails to the list and have them stored in the .msg format (so you can them in Outlook) and also have the email attributes promoted to SharePoint Columns.
There are a number of products in the market to assist, including OnePlaceMail where you can use the free express edition or the enterprise edition to save email to SharePoint libraries and lists. Both the free express edition and the enterprise edition will meet your requirement.
The following 2 articles may assist with the question of Outlook to SharePoint integration:
- One Way To Fix SharePoint's Outlook Problem (mentions OnePlaceMail and other 3rd party solutions) or
- Five out-of-the-box ways to get Email into SharePoint.
Email enabling a list may assist in some circumstance but you miss out on metadata and saving emails in the .msg format.
Please note: I am affiliated with OnePlaceMail.
