And to support and ensure that you constantly nurture mobile no database and engage your community, Facebook allows you to schedule posts on your Facebook group.
So, YES. Facebook allows you to schedule posts on your Facebook groups.
But;

How to schedule posts on a Facebook group
Easy peasy! Just follow these steps.
1. Go to the Facebook group where you’d like to schedule the post.
2. Then, click on create a public post in your Facebook Group.
3. Create the post by typing in your hen click the desired message, then click on the calendar icon at the button right part of the section. As shown in the diagram below.