How do I get my app to appear on this screen?
You must add a <intent-filter>
to the Activity statement in AndroidManifest.xml which includes action ACTION_SEND and the type of content it will treat .
Example for text type content:
<intent-filter>
<action android:name="android.intent.action.SEND" />
<category android:name="android.intent.category.DEFAULT" />
<data android:mimeType="text/plain" />
</intent-filter>
For more information, see Receiving simple data from other apps.