Java custom iterator for linked list

for uni we are supposed to implement an iterator for a String linked list by ourselves. But the infos how to do that was pretty small. So we tried it by ourselves and googled a lot but all the explanations we found dont include the whole code and I dont get how to implement the iterator correct. I think everything works fine as long as we use the for each loop to use the iterator but as soon as we are trying to use the "while (iterator.hasnext) { next }" thing it stays in the first element of the linked list. I think I know this problem is based on that we are always instantiating a new iterator but I dont get how to implement it else. Hopefully someone can help, I really don't know what to do, I tried everything..

import java.util.Iterator;
import java.util.NoSuchElementException;

public class LinkedList implements Iterable<String> {

     // ---------- Attributes ---------- 

     private int size = 0;
     private Node head = null;
     // private Iterator<String> linkedListIterator = this.iterator(); // ??

     static class Node {
    
        // ---------- Attributes ---------- 
    
        private String object;
        private Node next;
    
        // ---------- Constructors ---------- 
    
        public Node(String object, Node node) {
             this.object = object; 
             this.next = node;
        }
    
        public Node() { 
            this(null, null); 
        }
    
        // ---------- Getter, Setter ---------- 
    
        public String getElement() { 
            return this.object; 
        }
    
        public void setElement(String object) { 
            this.object = object; 
        }
    
        public Node getNext() { 
            return this.next; 
        }
    
        public void setNext(Node node) { 
            this.next = node; 
        }
    }

    class LinkedListIterator implements Iterator<String> {

        // ---------- Attributes ---------- 

        private Node currentNode = null;
        private int counter = 0;

        // ---------- Constructor ---------- 

        public LinkedListIterator(LinkedList linkedList) {
            this.currentNode = linkedList.head;
        }

        // ---------- Getter, Setter, Methods ---------- 

        public boolean hasNext() {
            return this.currentNode != null;
        }

        public String next() {
            if (!this.hasNext()) {
                System.out.println("Fehler: ");
                throw new NoSuchElementException();
            }

            String object = this.currentNode.getElement(); // ?
            this.currentNode = this.currentNode.getNext();
            this.counter++;
        
            return object;
        }
    
        public int getCounter() {
            return this.counter;
        }

    }

    // ---------- Getter, Setter, Methods ---------- 

    public Node getHead() {
        return this.head;
    }

    public void addFirst(String object) {
        // new node as head
        Node newNode = new Node(object, this.head);
        this.head = newNode;    
        this.size++;
    }

    public String getFirst() { //throws ListEmptyException {
        if (isEmpty()) {
            //      throw new ListEmptyException();
        }
        return this.head.getElement();
    }

    public String removeFirst() { //throws ListEmptyException {
        if (isEmpty()) {
            //      throw new ListEmptyException();
        }

        String object = this.head.getElement();
        this.head = this.head.getNext();
        return object;
    }

    public boolean isEmpty() {
        return this.head == null;
    }

    public int getSize() {
        return this.size;
    }

    @Override
    public Iterator<String> iterator() {
        System.out.println("helo");
        return new LinkedListIterator(this);
    }

    public String toString() {
        String output = "";

    //      this is working:
    //      for (String element: this) {
    //          output += element + "\n";
    //      }
    
        while (this.iterator().hasNext()) {
            System.out.println(this.iterator().hasNext());
            output += this.iterator().next() + "\n";
        }
    
        return output;
    }

    public static void main(String[] args) {
        LinkedList ll = new LinkedList();
        ll.addFirst("a");
        ll.addFirst("b");
        ll.addFirst("c");
        ll.addFirst("d");
        ll.addFirst("e");       
    
        System.out.println(ll.toString());
    }

}

Problem solved by this

But new question: Why is this working

public String toString() {
    String output = "";
    Iterator<String> iterator = this.iterator();

    while (iterator.hasNext()) {
        output += it.next() + "\n";
    }
    return output;
}

But this not

public class LinkedList implements Iterable<String> {

    private Iterator<String> linkedListIterator = this.iterator();

    public String toString() {
        String output = "";
    
        while (this.linkedListIterator.hasNext()) {
            output += this.linkedListIterator.next() + "\n";
        }
        return output;
    }
}