Assuming these are your own activities, you need to declare an action on the activity you want to be closeable, then call that action from the other app. The closing activity will get notified in onNewIntent() where you can check the action and call finish
In closable activity:
@Override
protected void onNewIntent(Intent intent) {
super.onNewIntent(intent);
if ("action.action.myactionstring".equals(intent.getAction())) {
finish();
}
}
In closeable activity mainfest
<activity android:name=".CloseableActivity" >
<intent-filter>
<action android:name="action.action.myactionstring" />
...
</intent-filter>
</activity>
In the other activity
Intent intent = new Intent("action string");
intent.addFlags(Intent.FLAG_ACTIVITY_SINGLE_TOP);
startActivity(intent);