When adding a User to a Usergroup, a user is also assigned to the Classic Role - "Standard User" this means that any Custom Roles created under Setup -> Admin -> Roles will require at a minimum Standard User permissions alongside the following permissions to be able to invite Users to Customer tenants using Usergroups:
This will allow that Role to then invite users to the Standard Users Usergroup which implements the Standard User Role Document.
As a minimum Custom Roles should be based on a copy of the "Standard User" Role within Setup -> Admin -> Roles.
For Custom Role Documents, and Role Documents such as Power User, and Administrator the Classic Role configured within the Partner tenant will also require any additional permissions that have been enabled for that Custom Role Document to be enabled within the Classic Role.