How to pass session from browser to a mobile app (Flutter)

I have a self-hosted Appwrite container. I also have a www page (A) which should acts as login page for different www services (B). User click login in B, is redirected to A, logs in, he is redirected back to A. On A is executed Appwrite function and Appwrite sets cookie with a session to the domain B. it works. But the same scheme doesn't work for the apps, in my case Flutter app. I want in Flutter to click login button, be redirected to the website A, login and be redirected back with working session (kinda like SSO works). So my question is: How to implement this? Currently it works for me only via JWT tokens, but they expire very soon. How to open session in the Flutter app after being logged in the browser? What is the exact algorithm? Thanx a lot for any help!