You can use the Piano API endpoint /publisher/team/list.
The API call should be in the following format:
https://api.piano.io/api/v3/publisher/team/list?aid=XXX&api_token=XXX
You would just specify the AID and the respective API token to get the data of the UID of the Team Manager member (to be inserted into the field manager_uids), e.g. for the API call /publisher/licensing/licensee/create.
In case your application's dashboard has another locale, the available base URLs are listed here.
The manager UID is actually the UID of the Team Member in the Team Manager.