Thanks for your question!
I’m not 100% sure about your question but I think you can accomply this with the use of a Singleton. Luckily, Guice has some some functionality for scopes. Here’s an example.

Main

public class Main {
    public static void main(String[] args) {
        Injector inj = Guice.createInjector(new MyModule());
        Payment pay = inj.getInstance(Payment.class);
        pay.setAmount("test");
        System.out.println(pay.getAmount());

        Payment pay2 = inj.getInstance(Payment.class);
        System.out.println(pay2.getAmount());
    }
}

Payment

public interface Payment {
    void pay();
    void setAmount(String amount);
    String getAmount();
}

CashPayment

public class CashPayment implements Payment {

    private String amount;

    public void pay() {
        System.out.println("Cash payment");
    }

    public void setAmount(String amount) {
        this.amount = amount;
    }

    public String getAmount() {
        return amount;
    }
}

MyModule

public class MyModule extends AbstractModule{
    @Override
    protected void configure() {
        bind(Payment.class).to(CashPayment.class).in(Scopes.NO_SCOPE);
    }
}

If you run this code, the output should be

test
null

There are 2 ways to implement the Singleton:
Mymodule

public class MyModule extends AbstractModule{
    @Override
    protected void configure() {
        bind(Payment.class).to(CashPayment.class).in(Scopes.SINGLETON);
    }
}

If you run the code again, the result should be

test
test

Secondly, you can implement the singleton inside the implenetationclass with an annotation

@Singleton
public class CashPayment implements Payment {

    private String amount;

    public void pay() {
        System.out.println("Cash payment");
    }

    public void setAmount(String amount) {
        this.amount = amount;
    }

    public String getAmount() {
        return amount;
    }
}

Hopely, this gives an answer to your question.

In your MyModule-Example you have this line:

arg0.bind(Payment.class).to(PaymentCardImpl.class);

now during the usage of the application, i want to do this:

PaymentCardImpl payment = new PaymentCardImpl();
payment.setPay(“currently calculated value”);
injector.OverwriteMyPaymentInstanceIntoGuiceWithThisNewInstance(payment)

When i use injection somewhere else and call getPay, i want to receive my previously stored information.

Is this possible?