Marc,
Wunderlist
For a simple ToDo list, take a look at Wunderlist (Windows, Andriod and iPhone). Multiple people can be using the same list. You can add tasks and assign them to somebody else and they show up on their list. It syncs via the cloud.
https://www.wunderlist.com/Keep in mind, however, Microsoft bought this and it is now a dead product. There haven't been any updates in a year and there probably won't be any more. Microsoft integrated some of Wunderlist's features in their ToDo list but not all, so Wunderlist is still a superior product.
Wrike
For something more sophisticated, look at Wrike (also for Windows, Android, and iPhone). This comes in various versions, with different capabilities. There is a free version for up to 5 users, but it's features are very limited. Even the free version is way more than a ToDo list, it is more like a private messaging system. You can define tasks and upload documents then invite others to respond and everyone invited can see the message thread and/or respond. When you leave a message for someone, they get a notification. The advanced versions have all kinds of other nice features. Nice system.
https://www.wrike.com/tour/It is probably worth looking at both of them.
James