I finally managed to fix it by using this filter:
add_filter('get_avatar', 'new_fb_insert_avatar', 1, 5);
function new_fb_insert_avatar($avatar = '', $id_or_email, $size = 96, $default = '', $alt = false) {
$id = 0;
if (is_numeric($id_or_email)) {
$id = $id_or_email;
} else if (is_string($id_or_email)) {
$u = get_user_by('email', $id_or_email);
$id = $u->id;
} else if (is_object($id_or_email)) {
$id = $id_or_email->user_id;
}
if ($id == 0) return $avatar;
$pic = get_user_meta($id, 'fb_profile_picture', true);
if (!$pic || $pic == '') return $avatar;
$avatar = preg_replace('/src=("|\').*?("|\')/i', 'src=\'' . $pic . '\'', $avatar);
return $avatar;
}
the get_user_meta($id, 'fb_profile_picture', true);
brings the user's custom avatar picture. Every user has a different picture, and it is stored in his user-meta information.