Q:

I have two inner class in class and i can't init class in swift

I can't init inner class. IDE me returning error, namely "'self' used before all stored properties are initialized". I attach picture where look error is ok

A:

The compiler is correct, you are attempting to pass self to the constructor of Customer before all stored properties are initialised, as SESSION won't be initialised until after the Session object is initialised, but that needs self - your two requirements are mutually exclusive.
You may need to rethink your architecture; If nothing else, the reference from Customer to Session combined with the reference from Session to Customer will give you a retain cycle and a memory leak.
If you want to use the current architecture, it is probably best to make the Customer property of Session a weak optional to avoid both your initialisation problem and the retain cycle;
class Customer {
    let session: Session
    let auth: Auth

    init() {
        self.auth = Auth()
        self.session = Session()
        session.customer = self
    }

    class Session {
        weak var customer: Customer?
    }
} 

You could make customer an implicitly unwrapped optional to avoid the need to unwrap it explicitly each time you refer to it, but you risk a crash if customer is released or not set:
class Session {
    weak var customer: Customer!
 }

On a point of style, Swift properties and variables should start with a lower case letter and use camel case, so auth, session and userID, not AUTH, SESSION and USER_ID.

