Instructions
Go to Business Integrations in Settings of your personal Facebook account (https://www.facebook.com/settings/?tab=business_tools)
Click on View and edit for Superchat
Tick all access permissions (having already selected the corresponding Facebook page).
Now go to Superchat and proceed to your Settings → Inboxes → Channel you want to update then select the three dots next to the channel and press Delete.
After that, you then need to connect the Messenger channel again, which you can find the instructions for here. This should update the settings and allow messages to come through.
Messages still aren't coming through
Messages still aren't coming through
In that case, ensure that messaging is enabled on your Facebook page. This is usually the cause of issues with Facebook Messenger.
You can enable Facebook messages by following the flow here.