Don't have 2013 on this computer, but take a look at http://www.addbalance.com/usersguide...ng_AutoCorrect for a utility to copy / edit / move AutoCorrect entries (unformatted and formatted).

The shortcut menu in spell-check was changed in Word 2013 (365). You are not finding the AutoCorrect option because it is not there.

Here are threads on this question.

http://answers.microsoft.com/en-us/o...9-75a98fd9d52e

http://answers.microsoft.com/en-us/o...da73b80?page=2

http://answers.microsoft.com/en-us/o...f-f6c3716b623f

http://answers.microsoft.com/en-us/o...1-b9bdfda0f04d

http://answers.microsoft.com/en-us/o...f-39d10cb36e43

The only fix suggested is to modify that menu using vba. Here is a link to the page that tells how to modify right-click (context) menus in Ribbon versions of Word.
Although it is written about Word 2007, the method will work with Word 2013.
http://gregmaxey.com/word_tip_pages/...tcut_menu.html

You would create a template that holds the code and use it as an Add-In.
Global Templates