Hello Alzander and Mati,
I have switched to a yootheme template but the problem remained unfortunately.
Following your recommendations and also
this post
, here's what I have done to have the Facebook Login button inside my mobile template:
1- added this code
$this['asset']->addFile('js', 'js:all.js');in /templates/yootheme_template/layouts/template.config.php where is says "
// add javascripts"
At this point, the JFB Connect module displays correctly when published in a mobile module position. Then I wanted to have the Facebook button in the original login module of the mobile template. So I looked for the proper template file to edit:
2 - added {JFBCLogin} in the login.php file in /templates/yootheme_theme/warp/systems/joomla/layouts/mobile, right before the end of the first
form tag
I hope this will help others. But at least this will help me redo these steps in the future

Please feel free to react if you see see something wrong.
Cheers.