1. if you look in the options for the admin menu module you will see an option to enable or disable the "Add New Shortcuts" this is done in code by using if ($createContent) so this PR would need that as well

2. The bigger problem is that when you use this new add module link it doesnt know if you are creating a site or an admin module. If the last filter used in the module manager was admin then the new module link will create admin modules etc (I think this is why the menu link was never created)

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   _{This comment was created with the J!Tracker Application at issues.joomla.org/joomla-cms/9845.}

Just some doubts @brianteeman
1. I went to module manager and set the Edit module option to "Administrator".

After coming back to Module dialogue box it was like this

The area i have marked in black rectangular box, should'nt it show "Modules(Administrator)"?
Maybe i had got a wrong idea, if u can clear.

2.I was unable to locate admin menu module option to enable and disable shortcuts. Could you point me in its direction.
Thanks in advance

Part 1

Part 2

Ohh! now i see!!
By directly adding a new module submenu confusion can occur whether it is for Administrator or for Site.

I think than this pull request is not necessary.

Btw I think there is a bug if you can confirm.

1. Click on the top-right "options" button
   

2. Select "Administrator" in edit module option.
   

3. After saving and closing it It still redirects to the "Modules(site)" page, I think it should redirect to "modules(administrator)" page.

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   _{This comment was created with the J!Tracker Application at issues.joomla.org/joomla-cms/9845.}

OK I will close this

As for your other issue. I dont think its a bug. clicking cancel or save always returns to the page you were on previously. The option you are selecting is to chose the default setting when you select modules from the menu