Wordpress multisite capabilities
João: By design WordPress user capabilities are restricted to a single site because many Multisite instances treat sub-sites as entirely separate entities. So in order to achieve what you want, you'll have to:


explicitly propagate users and their capabilities to the sub-site(s)
propagate the Groups plugin sync to the sub-site(s)


Task 1 is fairly straightforward: you'd use the civi_wp_member_sync_add_cap hook to detect when a capability has been added to a user. First add the user to your sub-site(s) with add_user_to_blog(), then switch_to_blog() and add the capability to the user before switching back to the current site.

Task 2 is a little more tricky. The Groups plugin states that "All features are supported independently for each blog in multisite installations". As a result (as you've discovered) the CiviCRM WordPress Member Sync plugin only syncs capabilities to the Groups plugin on the main site. To propagate that sync to the sub-site, you'll need to use the family of civi_wp_member_sync_rule_*_capabilities hooks and sync the capabilities to the Groups plugin instance on the sub-site(s) yourself. If it makes life easier, I can add some do_action calls in the relevant places so that you can guarantee that your code will run when expected.