This 'may' not be the proper way but I checked all the instal SQLs for the Photos module and only found the 'Set as Avatar' in the original 7.1 version.
I tested this on a demo and it worked but I strongly suggest that you backup your database BEFORE doing this (at least the sys_objects_actions table).
Step 1. Count how many buttons are in your actions block starting from 0 (zero). For example, the blue screenshot has 7 buttons in it.
Step 2. Login to your database via MyPhpAdmin or Webadmin from your control panel.
Step 3. Run the following script:
INSERT INTO `sys_objects_actions` (`Type`, `Caption`, `Icon`, `Url`, `Script`, `Eval`, `Order`) VALUES
('[db_prefix]', '{TitleSetAsAvatar}', 'image_link.png', '{evalResult}&make_avatar_from_shared_photo={ID}', '', 'bx_import(''BxDolPermalinks'');\r\n$o = new BxDolPermalinks();\r\nreturn $o->permalink(''modules/?r=avatar/'');', 8);
Step 4. Clear your cache.
The #8 at the very end of that script is the order of where the button will be placed. After you run it, it should look like the grey screenshot you provided.
AGAIN - This may not be the proper way but it worked. BTW, Both Avatar and Photo modules HAVE to be installed.