Exported menu blocks to a feature module via FE block they are not created - Why?
You need to select also, in the feature, under strongarm, the "menu_block_ids" variable. Also make sure that the dependency to strongarm is selected. Sometimes it shows the select box but it is left unchecked. 

With that the menu block should appear in the blocks page. 

It will not appear in the context->edit->menu block though, and I think that is an issue. I am doing more tests before I really open it though.

----alternatively 

Don't do it with fe features or strongarm, instead, just use menu block export module (go there admin/config/user-interface/menu-block/export) and proceed, just put any name and click export.

Copy the resulting code in your feature.module (make sure you put the proper name). Something like this:

function feature_name_menu_block_blocks() {
// The array key is the block delta used by menu block.
  return array(
    '23' =&gt; array( // feel free to change this to the real id of your menu block
      'parent'      =&gt; 'menu-api-menu:0',  //the module might not encapsulate string, be careful
      'title_link'  =&gt; 0,
      'admin_title' =&gt; 'title',
      'level'       =&gt; 1,
      'follow'      =&gt; '0',
      'depth'       =&gt; 0,
      'expanded'    =&gt; 1,
      'sort'        =&gt; 0,
    ),
  );
}


Just copy the menu block you want to export, you dont have to copy all of them.