Short cut key for Content-Aware Fill

The reason why nobody is talking about it is probably because you can easily do that yourself. As others have already said; you can (re)assign shortcut keys in Photoshop yourself. Another option is to record an action and assign a key to that, so you can even have multiple steps that are performed after pressing a shortcut key. I have an action to fill empty areas. Because just filling an empty area often leaves a one pixel line, my action does the following: it expands the selection by one pixel, the applies 'Fill - Content Arare', and then deselects.

The shortcut I use is Shift+Backspace. That opens the Fill dialog box. Contents are set to whatever was used last and because I use Content-Aware, that is always the default. Press Enter to accept.

If you are using Mac, I believe that the shortcut would be Shift+Delete, then press Return.

This is not a custom shortcut. It is already built into Photoshop.