In order to publish posts as your business page, you need to join the group as your page and make it admin in the group.
This is most easily done from a computer or laptop, if at all possible.
1. Make sure your personal profile is an Admin in the group - this is necessary for the next steps.
2. Check the Group Settings:
- Under Set Up Group: ensure that it is visible (not hidden - it can stay private though)
- Under Manage Membership (sometimes labeled Participation instead), make sure that both Pages and Profiles can join groups.
Note: This would be a good time to copy the link at the top of the Facebook group, for easy navigation in the next step.
3. Join the group, as your business page name:
In the top corner of your Facebook screen, click your profile picture and switch to interacting as your business page.
Navigate back to your Facebook group. (The quickest way to get there is to paste the link you had copied when recommended above.)
Look for the Join Group button, and click it.
4. Approve your business page's request to join:
In the top corner of your Facebook screen, switch back to interacting as your personal profile.
From the lefthand control panel, check the Member Requests tab to approve your page as a member.
5. Lastly, make your business page an admin of that group:
Click the Members or People tab at the top of that group.
Locate your business page's name
Click the 3-dot icon beside your business page's name
Select the Add or Invite as Admin option
In the top corner of your Facebook screen, click the profile picture to swap back to interacting as your business page.
There will now be a banner near the top of that group where you can accept that admin invite. It may also be in your Facebook notifications as well.
Once the group shows your business page as an admin of that group, you will be able to publish posts as your business page profile.