My company has been using SharePoint Server for a few years now. Everyone was comfortable with it and following a set of processes. We decided to migrate to the cloud to get the server maintenance off our back and to take advantage of the many features available in SPO.
One of our departments has been using Discussion Boards and forwarding emails into SharePoint 2013 to archive emails, be able to "process" and count them and to easily access them if ever needed. After the migration, we found out you can no longer email things into lists - and boy was my world turned upside down when this was noticed. After many days of research, trying things out, and failing, I just never could find a good solution. Finally, I was working on something for someone else one day and it hit me - Connect to Outlook.
I tested it - created a test list, connected to Outlook and drag and dropped - and BAM - it was there (after a second of syncing of course). There are some known drawbacks (I will list below), but it seems to work well, and do what 
I/they want it to do! They are now archiving emails into SharePoint by using Outlook 2016/2013 and a simple drag and drop - but now, they can do multiple at a time!
Known Drawbacks
- Moving the file will only attach the EML and require you to click "Post". Copying does not require this or do this
- The user must have at least contribute permission
- In order for the user to delete messages that other users have put there (the person originally doing it decided to hand it off to another employee), you must set Create and Edit access to All Items in advanced settings (even if they have Edit permissions) because it is set to Only items created by user by default
If you find any other drawbacks - please let me know and I will add them. Hope that saves you some time! It took me many days to figure that out!
Originally posted at https://moreabout.tech/adding-emails-into-sharepoint-online-discussion-boards/