Using the web based Office 365 as a mailto: link via a web browser looks like this functionality is not fully supported as this configuration is not a standard setup of Office 365.
It may be possible if an update has been made - please find a link below to a section on using web mail services with Firefox browser where you may or may not be able to find some information on linking to the web based Office 365:
https://support.mozilla.org/en-US/kb/change-program-used-open-email-links
You can however use the Office 365 software programme if it is locally installed onto a Windows PC to set up as a default mailto handler. You will need to set this up via your default programmes on your PC - so that for Email you select 'Office 365' as the default mailto handler.