Hi,
Please consider to add Web Push notifications in Firefox.
https://support.mozilla.org/en-US/kb/push-notifications-firefox?as=u&utm_source=inproduct
“Web Push allows websites to notify users of new messages or updated content. While Firefox is open, websites who have been granted permissions can send notifications to your browser and display them on the screen. Users can easily allow or disable notifications and control how these notifications appear.”
Regards,
Our developers agree that this is a great idea. 
Added issue #904 in our issue tracker for this.
– Geir
Thanks,
I’m sure this feature is browser dependent. but yeah to fully replace the email client on the desktop and mobile the Web Push notifications is something to look at… I already abandon the desktop client…
I have an app password just for the email client on the phone to notify me when I received an email, then the phone is connected to my linux desktop (KDE Neon) using KDE connect on the Android Phone, I get all the notifications, I’m happy, but I see app password as a security issue. So having the Runbox app integrated with Firefox notifications will be Awesome!
May be you want to look if other major browsers have something like this, not everyone uses Firefox…
Regards and Thanks again to consider this.
Yes, we are planning to implement this in all major browsers.
– Geir