admin menu items visibility to a role (enable access of admin button to other admin role)

Hi,

In default settings, only the role of administrator can access "admin" button (as attached image). Is it possible to let other role to see it? I would like to let a special role be be able to access admin menu (through menu button at oa_toolbar) for security reason (some people can configure some parts of the web site but not as administrator).

For example, I had following configuration in the following:

1) at oa_toolbar_panel, open Atrium ToolBar Menu Button is enabled (with no rule)
2) a special role shop_admin created

The special role Shop_admin cannot access the admin button.

I even set shop_admin role can "admin" the menus, so the user with that role can access every menu. However, I found that the user cannot see the items (it is empty) in the management menu; therefore, the user cannot see the menu button??? How can I enable the access to the role? Is this setting of an permission item? I spent lots of time and cannot find it. Any information would be appreciated.

Note:
1) The menu is not enabled as a block.
2) There is "edit block" in the setting of penalize (ToolBar Menu button of /admin/structure/mini-panels/list/oa_toolbar_panel/edit/content). All the access is open.