We'll keep it short and simple: here's how to do it and, above all, which platform lets you do it automatically.
Go to https://farsem.net, create your account, and the rest is in pictures:
Farsem.net lets you publish automatically to multiple Facebook groups. You can send "Immediate" or "Scheduled / recurring" posts, set start and end dates, and schedule several weeks with a different post.
Choose the groups you want to post to and define your target from the groups you belong to as a member or admin. Set the days and times for your posts in the selected Facebook groups.
We offer very advanced human-simulation features, such as randomising the image order in each post.
Create your free account to see and learn more at https://farsem.net.