Want to do local storage with login details

Question

Currently, I am trying to store the email and password that is entered. Below I have the HTML and JS code

let email = document.querySelector(".email");
let password = document.querySelector(".password");

//Storing users email and password
function store()
{
    localStorage.setItem('email',email.value)
    localStorage.setItem('password', password.value)
}

function checkLogin()
{
    //get set stored data
    let emailStored = localStorage.getItem('email')
    let passwordStored = localStorage.getItem('password')

    //data entered from login-form
    let emailInput = document.querySelector('.email').value
    let passwordInput = document.querySelector('.password').value

    if(emailInput != emailStored)
    {
       let eError = document.querySelector(".email-error-message")
       eError.innerHTML = "Please enter valid email address"
    }

    if(passwordInput != passwordStored)
    {
        let pError = document.querySelector(".password-error-message")
        pError.innerHTML = "Please enter password associated with email address"
    }

}

<div class="login-form">
  <div class="sign-in">
    <h1>Sign In</h1>
    <form class="form">
      <input class="email" type="email" placeholder="Email Address" required />

      <div class="email-error-message"></div>

      <input class="password" type="password" placeholder="Password" minlength="6" required />
      <div class="password-error-message"></div>

      <button class="submit">Sign In</button>
      <div class="remember-me">
        <input class="checkbox" type="checkbox" />
        <span class="remember">Remember me</span>
        <span class="need">Need help?</span>
      </div>
    </form>

    <div class="facebook-signin">
      <img src="images/facebook_social media_social_icon.png" alt="facebook logo" />
      <span class="flogin">Login in with facebook</span>
    </div>
    <div class="newNetoflix">
      <div class="newToNetflix">New to Netflix?</div>
      <a class="sign-up" data-uia="login-signup-now">Sign up now.</a>
    </div>

    <div class="disclaimer">
      <span class="protected">This page is protected by Google reCAPTCHA to ensure you're not a
        bot.&nbsp;</span>
      <button type="submit" class="learn-more">Learn More</button>
    </div>
  </div>
</div>

My end goal is the following:

• when the user inputs their email address and password it is saved
• when user clicks the check box of remember me it keeps their email address there, but not their password.

PS: I am aware there needs to be an event listener with the checkbox, saying that when the checkbox is checked keep email when the browser refreshes.