передать значение в input?

let options = document.querySelectorAll('.category_parent_id');
let catId = document.querySelector('#category_id');
let catName = document.querySelector('#name');
let save = document.querySelector('.btn-save');
let valId = null,
  valName = null;

save.addEventListener('click', () => {
  catId.value = valId;
  catName.value = valName;
})

for (elem of options) {
  elem.addEventListener('click', (e) => {
    valId = e.target.id;
    valName = e.target.innerHTML;
  })
}

<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/css/bootstrap.min.css" integrity="sha384-ggOyR0iXCbMQv3Xipma34MD+dH/1fQ784/j6cY/iJTQUOhcWr7x9JvoRxT2MZw1T" crossorigin="anonymous">

<form method="post" action="" class="form-horizontal form-bordered">
  <div class="card-body">
    <div class="form-group">
      <label for="name">Название категории</label>
      <input type="text" class="form-control" id="name" name="name">
    </div>
    <div class="form-group">
      <label for="parent_id">Родительская категория</label>
      <button type="button" class="btn btn-primary btn-open" data-toggle="modal" data-target="#exampleModal">
                Выбрать категорию
            </button>
      <input type="hidden" name="parent_id" value="" id="category_id">
    </div>
  </div>
  <!-- /.card-body -->

  <div class="card-footer">
    <button type="submit" class="btn btn-primary">Добавить</button>
  </div>
</form>

<div class="modal fade" id="exampleModal" tabindex="1" role="dialog" aria-labelledby="exampleModalLabel" aria-hidden="true">
  <div class="modal-dialog" role="document">
    <div class="modal-content">
      <div class="modal-header">
        <h5 class="modal-title" id="exampleModalLabel">Modal title</h5>
        <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                    <span aria-hidden="true">&times;</span>
                </button>
      </div>
      <div class="modal-body">
        <ul style="list-style: none">
          <li><a class="category_parent_id" id="1" style="cursor: pointer">Категория 1</a></li>
          <li><a class="category_parent_id" id="2" style="cursor: pointer">Категория 2</a></li>
          <li><a class="category_parent_id" id="3" style="cursor: pointer">Категория 3</a></li>
          <li><a class="category_parent_id" id="4" style="cursor: pointer">Категория 4</a></li>
          <li><a class="category_parent_id" id="5" style="cursor: pointer">Категория 5</a></li>
          <li><a class="category_parent_id" id="6" style="cursor: pointer">Категория 6</a></li>
        </ul>
      </div>
      <div class="modal-footer">
        <button type="button" class="btn btn-secondary" data-dismiss="modal">Close</button>
        <button type="button" class="btn btn-primary btn-save" data-dismiss="modal">Save changes</button>
      </div>
    </div>
  </div>
</div>

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