Finish an activity from another activity

1. Make your activity A in manifest file: launchMode = "singleInstance"

2. When the user clicks new, do FirstActivity.fa.finish(); and call the new Intent.

3. When the user clicks modify, call the new Intent or simply finish activity B.

FIRST WAY

In your first activity, declare one Activity object like this,

public static Activity fa;
onCreate()
{
    fa = this;
}

now use that object in another Activity to finish first-activity like this,

onCreate()
{
    FirstActivity.fa.finish();
}

SECOND WAY

While calling your activity FirstActivity which you want to finish as soon as you move on,
You can add flag while calling FirstActivity

intent.addFlags(Intent.FLAG_ACTIVITY_NO_HISTORY);

But using this flag the activity will get finished evenif you want it not to. and sometime onBack if you want to show the FirstActivity you will have to call it using intent.