You want to change the Group Manager of a group but when you go looking for the option 'Change Group Manager' your quest will be futile. There is no option within Organic Groups bearing such a description. You will have to look further and deeper... or simply read this blog post. It's quite easy but as far from logical as possible.

In order to use Organic Groups with Drupal 7 you have to determine which Content Type will be a 'Group Type' as shown below (you can do this by either creating or editing a Content Type):

So now you have assigned a certain Content Type as a 'Group Type'. Here comes the fun part: The user who creates a new node of this Content Type will be automatically the Group Manager. This is because, the author of the node is the Group Manager. In order to change the Group Manager simply change the Author of the node to the user you want to be the Group Manager:

It's not difficult, you just need to know where to look.

Drupal 7Organic Groups