At a first glance, WP-Filebase only allows you to limit access by User Roles, but not User Groups added with 3rd-party plugins, such as UAM. Here’s how to setup WP-Filebase Pro and the User Access Manager Plugin to set permissions for User Groups.
In the UAM Plugin you can set “Role affiliation” for each user group. Create a User Role for every user group and set respective affiliation. In WP-Filebase you can then limit access to the created User Roles, thus the affiliated User Groups.