There are lots of ways to share and track tasks among teams, and this is probably one of the most rudimentary (ie. least feature packed). But I have tested it, and it does actually work. Basically, you install a script from the instructions below, and it allows you to share a given Google task list with selected people.
Scroll down to How to Create a Shared Google Task List? and follow the steps after clicking below:
Shared Google Tasks: How to Share and Sync your Task List with Others