Custom module with related list does not show related list in shared contact records

The problem:

We have a custom module, called "licensing". This licensing module has a related "lookup field" for the account associated with the licensing record. As an admin, when you open an account, you can see the licensing module and related list.

For users with "shared records", the licensing module appears fine but empty. When I open an account with a license as the record owner, the license list is "blank". If I open the same account with an admin login, I can see the related records/licensing module details populated.

I have confirmed:

in setup, modules, the permissions to access this module are turned on for the profile related to the user
in setup, users, security control, the profile does have permissions to the module (note changing or turning off detailed permissions seems to make no difference)

I did find this note " The following records associated as related list will not be shared: closed activities, invited events, products, campaigns, contact roles, related lists added as part of an integration." on this page , but am very hopeful that related lists as part of an integration means all related lists. If you have the opinion that is the problem, any suggestions on how to manage that or workarounds?

Thanks in advance for any help!