You cant control the other db but you can implement your own user table and make sure its hashed correctly
- get login form from user
- attempt login. if it works then all is good, redirect them within your application
- if login fails, check if there is a local account for them. If so then password must be keyed wrong, return error
- see if you can validate username and password against other database
- if not, return error as earlier
- if username and password were correct, create local user account, hash their plaintext password and log them in to laravel
- redirect as per your earlier success path
considerations
- you must know how the password is stored in the other system
- users have two distinct login credentials. over time their passwords coukd be out of sync