Update 2016: I’ve since found a better way to do Google Group to Discourse migrations and have written an updated howto here:
Someone who knew more about Google Groups had managed to make a script which can extract the messages from a Google Group as a series of .mbox files. Discourse already has an importer for these .mbox files.
I wrote a fairly hacky script which connects the exporter to the importer, for a more seamless migration. Please do contact me if you’ve tried the script, I’d like to know it’s being used, and of course if you have any problems too please contact me and I’ll try to help.
Back in 2015, eHealth Insider (shortly afterwards rebranded Digital Health Intelligence) were working on a new Social Collaboration Platform for the CCIO Network and Health CIO Network. We experimented with various platforms including Drupal Commons and Open Atrium (both of which were too complex to set up and have looking nice, without having to become a PHP dev, which nobody really wanted 
)
We eventually settled for Discourse (and the rest is history). As part of this I had to migrate the existing CCIO Leaders’ Network and Health CIO Networks over from the Google Groups they are in over into Discourse.
Discourse has a nice REST API so the Discourse end of things was pretty easy. On the Google Groups side, it proved very difficult to extract the content of the messages cleanly. I tried a variety of approaches but ended up having to scrape the content from the viewed, rendered pages using Selenium Webdriver (really a web testing tool, not a scraping tool)
The deprecated original script I used is here
Here’s a screencast of how it looked as Selenium iterated through all the pages in the Google Group while it scraped them and sent them to Discourse.