Japanese input on 16.04 with Fcitx and Mozc

Typing Japanese on Ubuntu used to mean ibus-mozc, but ibus-mozc has been less and less maintained since 2015:

Ubuntu 15.10 is supposed to start using Fcitx rather than ibus as their default input method (input method framework), which is another reason for me to hesitate to spend my time to improve ibus-mozc

This official documentation page claims that Fcitx has become the default:

Recommended frameworks for input methods are IBus and Fcitx. The latter is the default framework in Ubuntu for Chinese, Japanese, Korean and Vietnamese.

This claim is disputed, but even if not default, now after upgrading from 2015.10 to 2016.04 ibus-mozc has a problem that makes it unusable for me, so I would like to switch to fcitx-mozc.

QUESTION: How to switch Ubuntu 2016.04 from ibus-mozc to fcitx-mozc?
I see a fcitx-mozc 16.04 package, but I guess there is more to do than just installing the package? What is the recommended procedure?

1. Install Japanese. One of the installed packages is fcitx-mozc.
2. Close Language Support and open it again.
3. Select fcitx as the Keyboard input method system.
4. Log out and log in again.
5. Click the icon at the very right of the menu bar and select System Settings.
6. In the Personal section, click Text Entry.
7. Click the + button, select Mozc (Fcitx), and click Add.

More info