Refactoring Guru chain of responsability in rust with reference to objects

Question

I'm trying to implement the chain of responsibility from refactoring guru

https://refactoring.guru/design-patterns/chain-of-responsibility/rust/example

But instead I need to pass the object by reference as they need to be called later on

    let cashier = Cashier::default();
    let medical = Medical::new(&cashier); // instead of Medical::new(cashier)

But I'm having a hard time dealing with lifetimes, and references. To give a bit of detail, I get stuck here

pub(self) fn into_next(
    department: impl Department + Sized + 'static,
) -> Option<Box<dyn Department>> {
    Some(Box::new(department))
}

because trying to modify the parameter type to accept a reference leads later on to cannot borrow data in a & reference as mutable. when trying to execute the next method

fn execute(&mut self, patient: &mut Patient) {
        self.handle(patient);

        if let Some(next) = &mut self.next() {
            next.execute(patient);
        }
    }

what I've tried:

• removing all the Box as i want to work with references and from what I understand Box take in the trait itself.
• adding 'static pretty much everywhere vscode wanted me to put some life times
• added more scoped lifetimes ('a) where vscode told me after the 'static did not work
• ... and other stupid things that obviously would not work because i'm loosing it...

If you need the code to run it, I'd recommend you clone the repo https://github.com/RefactoringGuru/design-patterns-rust/tree/main/behavioral/chain-of-responsibility