How to make my app be listed as a "Source" for the "Attach" Intent menu of another app?

I already know how to invoke an Intent to "share" something my app generated to another app using an Intent.

But, I would like to know how to have my app listed in what I would call the "Source" app list of another app.

Meaning, when you are in an SMS/TEXT messaging app, and you click the "Attach" button, it pops up a list of apps that can "generate" an attachment, such as the Camera app, or Gallary app.

How can I register my app so it will be listed in such a menu?

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