The crosspost is implemented without Google+ API, without Chrome app.
Google plus post is updated programmatically using PHP, cURL.
The script can be put to cron for automatic Twitter 2 GooglePlus crossposting.
The code works for me perfectly, yet doesn’t work when 2-step verification is ON.
Check/fork it here: https://github.com/DmitrySandalov/twitter2gplus
Credits:
Luka Pusic (luka@pusic.si)
Vladimir Smirnoff (mail@smirnoff.sumy.ua)
Sergey Pashko aka Kichrum (http://kichrum.org.ua)