At this moment it's not possible to compose and publish Facebook Stories with Agorapulse.
However, there is a little hack you could use. You can first publish a Story on Instagram and then re-share it on your Facebook Page. How to do this?
First, you need to check how to publish Stories to Instagram with Agorapulse - read more here.
When you are finishing your Story on the Instagram app, you can tap and hold on to the Your story button and select to share to Your Facebook Story. This will then automatically share your stories to Facebook each time.