If you want to use Natterbox permission sets in permission set groups you must manage permissions via the Salesforce admin console and not through Natterbox.
In order to do this you need to enable the setting in the Natterbox Account Settings tab. Head to Account Settings and edit the record.

Clicking the checkbox shown above will turn on this feature. When enable the feature you will get a pop up message that you must confirm

Once enabled if you go to a Natterbox user record, you will now see a notification where the permission level drop-down used to be.
Before the setting is enabled

After the setting is enabled

Once enabled, you will need to have a Salesforce Admin manage permissions by using the NBAVS permission sets detailed in previous chapters.
Natterbox will not change any permission sets granted to any users when enabling this setting.
Disabling the setting
If at a later stage you decide to disbale the setting and go back to a system where you are managing Natterbox permissions via the Natterbox app simply uncheck the box in the Account Settings tab again.
You will get the following message telling you that Natterbox will run an Apex Job with the scope “BatchUpdateUserScopes”, which runs through all of the permission sets applied to each user in Salesforce and ensures the drop-down on the User tab in Natterbox reflects the highest level of permission granted to that user.

Syncing Salesforce and Natterbox Permissions
Whilst you do not have to do this at any time (the system will run a sync job when it is needed) you will see some Sync buttons when the setting is enabled.
Account Settings

Natterbox Users

Clicking on either button will sync Natterbox with Salesforce, so it will run a job to take the highest level of permission set provided in the Salesforce permission sets, and assign that level to the user. The only time you might need to use these buttons is if you have many apex jobs running and the Natterbox sync job has been delayed.