If it is a regular HTML button/link, not something inside the Flash plugin, you probably can do it with an extension or a user script.

You can search for relevant extensions here: https://addons.mozilla.org/firefox/extensions/

These are forums where you can seek help with getting a user script created for you:

• https://greasyfork.org/en/forum/categories/script-requests
• https://openuserjs.org/corner

If those are not immediately successful, you could look into the wide range of programs that can manipulate or embed Internet Explorer.

There are other things that need attention.

The System Details list next to the question shows that you have an outdated Shockwave Flash plugin.

• Shockwave Flash 12.0 r0

You can download the latest Flash player version for Firefox via this page:

• https://get.adobe.com/flashplayer/otherversions/

Maybe you can do this with a bookmarklet as well (that would require to click the bookmark).