Hi Janes,
As your description, you want to share some emails that send to you to other users. The emails are transferred to specific files and then stored in SharePoint Online site, you want all the users can access them directory without save them firstly. If I misunderstand, please feel free to correct me.
Moreover, do you have Office desktop application set up on end users’ computer, such as Office 2007? If so, please provide the Office desktop application version.
If this is the case, we may achieve these goal by Outlook and OneNote desktop application. Generally, we can create a OneNote file at a team site document library. Then, the email received can be sent to that OneNote file via Outlook. After that, the other users can open that OneNote file at the team site to see the those emails.
Thanks,
Eben Liu