Constructor Injection Pattern needed

I have a set of 3 nested classes where the 'inner' classes are instanciated in the constructor of the 'outer' classes. In the constructors, I want to pass variables from the outer class to the inner, so the inner classes can use them:

<?php
class A
{
    protected $vars = ['a_var' => 'var_from_a'];

    public function __construct($context = [])
    {
        $this->vars = array_merge($this->vars, $context);
        $this->b = new B($this->vars);
    }

    public function get()
    {
        return $this->vars['a_var'] . '<br>' . $this->b->get();
    }
}


class B
{
    protected $vars = ['b_var' => 'var_from_b'];

    public function __construct($context = [])
    {
        $this->vars = array_merge($this->vars, $context);
        $this->c = new C($this->vars);
    }

    public function get()
    {
        return $this->vars['a_var'] . '/' . $this->vars['b_var'] . '<br>' . $this->c->get() ;
    }
}


class C
{
    protected $vars = ['c_var' => 'var_from_c'];

    public function __construct($context = [])
    {
        $this->vars = array_merge($this->vars, $context);
    }

    public function get()
    {
        return $this->vars['a_var'] . '/' . $this->vars['b_var'] . '/' . $this->vars['c_var'] . '<br>';
    }
}

$a = new A();
echo $a->get();
?>

// var_from_a
// var_from_a/var_from_b
// var_from_a/var_from_b/var_from_c

So far so good, but I want to change the class method get() of class B to the following:

class B
{
    /* ... */
    public function get()
    {
        /* insertion here */
        $this->vars['b_var'] = 'hurray';
        /* insertion here */
        return $this->vars['a_var'] . '/' . $this->vars['b_var'] . '<br>' . $this->c->get() ;
    }
}

// var_from_a
// var_from_a/hurray
// var_from_a/var_from_b/var_from_c

So my question is: Is there a pattern, maybe something with referenced variables, to get this result instead:

// var_from_a
// var_from_a/hurray
// var_from_a/hurray/var_from_c 

I want to change the already passed variable in class C from a method of class B.