I'm dealing with Exchange Online (Outlook 365), hence, I have no access to the email server at all.
However, I took another path. @TotallyInformation's hint regarding PowerApps was a good one.
Microsoft Flow takes advantage of Exchange Online push notifications. So, I created a flow that writes the email attachment to DropBox every time a new email arrives in the specific folder:
In NodeRED, with the help of
node-red-node-dropbox I check for a new file in the DropBox folder, download it and send it to the Telegram chat:
It works like a charm! 
Thanks to all of you for your contributions and the many creative ideas!
