Please provide a screenshot of that "Win8.1 mail screen".

See this support article. How do I create a screenshot of my problem? It is best to use a compressed image type like PNG or JPG to save the screenshot and make sure that you do not exceed a maximum file size of 1 MB.

Then use the Browse .... button below the Post a Reply text box to upload the screenshot.

Relative to settings or choices within Firefox, see this support article. https://support.mozilla.org/en-US/kb/change-program-used-open-email-links

Attached

That looks like a screen for "default web mail", not for "Default Programs". Thunderbird needs to be set as the Default Program for email in Windows for it to appear in Firefox as an email client for you to select.

I'm going to move this thread over to the Thunderbird support questions queue.