It depends on that social buttons plugin and if it also uses the_content filter.
I believe someone has already posted a solution to this and it's somewhere in the forum, but you need to find it.
Basically, you need to change the ts-fab.php (Plugins > Edit > Fancier Author Box). Locate this line:
add_filter( 'the_content', 'ts_fab_add_author_box', 15 );
and change that number 15 to a bigger number. Try several numbers until you achieve what you need.
I don't suggest you do this if you're not familiar with PHP. Also, you'll need to do this every time you update the plugin.