1. In order to unblock someone from a Facebook group, sign in to Facebook using the account you use to manage the group, and then navigate to the group using the left sidebar. By default, Facebook does not show all of the groups that you have joined or managed. If you cannot find the group you want, click More to access the full group list.
2. Once you are in the group, find and click on the Members tab. This tab is a hub for accessing information regarding all of the group’s members.
3. When the list of members shows up onscreen, click the All Members button near the search box to see more options, and choose Blocked.
4. Clicking the Blocked option will filter out all the group members but the ones you have blocked. Here, you can find a list of all Facebook users that you and any other admin have blocked from the group. No matter when you blocked them, Facebook will still keep a list of blocked members for you. To find the member you want to remove from the list, use the Search button near the Blocked button. To lift the ban for that particular user, click the Remove Ban link near his profile picture, and then click Remove Ban again in the pop-up window to confirm.
5. When the user has been successfully removed from the list, you can search and manually add him back to the group as if nothing ever happened.
How Can I Unblock Someone from a Facebook Group?