ibarmin

I’ll look into this

Also, note, that configuration is per blog,

you (or owner of that blog) have to enable respective buttons in Settings > WP Easy Embed for that blog.

So, one blog has oEmbed Provider installed and you want to embed posts from it on second blog, that has WP Easy Embed installed, right?

For second site you should read this:
http://codex.wordpress.org/Embeds#Adding_Support_For_An_oEmbed-Enabled_Site
and add something like this

<?php
$sourceBlog = trailingslashit('http://example-blog.com/'); //if you installed wordpress in a folder, not in a root - add path to that folder
$format = $sourceBlog . '*';
$provider = $sourceBlog . 'wp-content/plugins/oembed-provider/oembed-provider.php';
wp_oembed_add_provider($format , $provider ); ?>

in your code (either in a plugin or in a theme functions.php file).