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public class YourActivity implements FragmentA.TextClicked{
    @Override
    public void sendText(String text){
        // Get Fragment B
        FraB frag = (FragB)
            getSupportFragmentManager().findFragmentById(R.id.fragment_b);
        frag.updateText(text);
    }
}


// Fragment A defines an Interface, and calls the method when needed
public class FragA extends Fragment{

    TextClicked mCallback;

    public interface TextClicked{
        public void sendText(String text);
    }

    @Override
    public void onAttach(Activity activity) {
        super.onAttach(activity);

        // This makes sure that the container activity has implemented
        // the callback interface. If not, it throws an exception
        try {
            mCallback = (TextClicked) activity;
        } catch (ClassCastException e) {
            throw new ClassCastException(activity.toString()
                + " must implement TextClicked");
        }
    }

    public void someMethod(){
        mCallback.sendText("YOUR TEXT");
    }

    @Override
    public void onDetach() {
        mCallback = null; // => avoid leaking, thanks @Deepscorn
        super.onDetach();
    }
}

// Fragment B has a public method to do something with the text
public class FragB extends Fragment{

    public void updateText(String text){
        // Here you have it
    }
}