Is there a way to modify a string external to a closure without having that closure take ownership of it?

Question

I'm trying to write a simple calculator app to get the hang of FLTK, specifically the Rust binding. For the output I want to store a string somewhere that I can have an output set to, that way it's a little more simple to handle, but, the compiler really doesn't like that.

I'm trying to use a callback for this in a loop since I need to do it ~9-10 times for all the buttons and I would like to be able to repeat it for larger button amounts that need some standard callback.

I have tried doing the compiler's suggestion of having the closure take ownership with move but the problem with that is I can't get the string back out to use later, since the library makes it so the function can't have a return value on top of that it doesn't make sense to hand over ownership to anonymous function that can't hand it back.

A fragment of the current code I have in my compiler is

fn main() {

    let mut number_buts: [Button; 10] = arr![Button::default(); 10];
  
    let mut out_string: String = String::new();
    for i in 1..number_buts.len()
    {
        let mut current_but = Button::default();
 
        let call_back = |but: &mut Button| {
            out_string.push_str(but.label().clone().as_str());
        };

        current_but.set_callback( call_back);        
        let _ = mem::replace(&mut number_buts[i], current_but);
    }
}

The error I get is

error[E0373]: closure may outlive the current function, but it borrows `out_string`, which is owned by the current function
  --> src\main.rs:46:25
   |
46 |         let call_back = |but: &mut Button| {
   |                         ^^^^^^^^^^^^^^^^^^ may outlive borrowed value `out_string`
47 |             out_string.push_str(but.label().clone().as_str());
   |             ---------- `out_string` is borrowed here
   |
note: function requires argument type to outlive `'static`
  --> src\main.rs:50:9
   |
50 |         current_but.set_callback( call_back);
   |         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
help: to force the closure to take ownership of `out_string` (and any other referenced variables), use the `move` keyword
   |
46 |         let call_back = move |but: &mut Button| {
   |                         ++++

error[E0499]: cannot borrow `out_string` as mutable more than once at a time
  --> src\main.rs:46:25
   |
46 |         let call_back = |but: &mut Button| {
   |                         ^^^^^^^^^^^^^^^^^^ `out_string` was mutably borrowed here in the previous iteration of the loop
47 |             out_string.push_str(but.label().clone().as_str());
   |             ---------- borrows occur due to use of `out_string` in closure
...
50 |         current_but.set_callback( call_back);
   |         ------------------------------------ argument requires that `out_string` is borrowed for `'static`