By the time the user logs in through the authase auth system and receives a response, your application should send the registered user information to the api register offered by wordpress in order to register this user in the wordpress system. You also need to study the implementation of the wordpress function wp_set_auth_cookie
in order to mock the cookie for clients, the cookie value may be part of your api response in wordpress register. After receiving the cookie value, the android must manipulate the cookie and save the cookie in a web browser in order to automatically enter the Wordpress firewall system.