Why not use the "User agent Switcher" plugin ?
See : https://addons.mozilla.org/fr/firefox/addon/59

Just set your user agent to an IE signature. The server will think
you have an Internet explorer ... But it could cause problem with
some scripts and any activeX. So, test it with your problem site to
see if it works... It depends how they check the browser ID : with
some script or with the user agent string.