add_action( 'wp_ajax_nopriv_ajax_login_func', 'ajax_login_func' );
add_action( 'wp_ajax_ajax_login_func', 'ajax_login_func' );
function ajax_login_func() {
    $username = sanitize_text_field($_POST['user']);
    $password = sanitize_text_field($_POST['password']);

    $creds = array();
    $creds['user_login'] = $username;
    $creds['user_password'] = $password;
    $creds['remember'] = true;
    $user = wp_signon( $creds, false );
    if ( is_wp_error($user) ) {
        echo 0;
        die();
    }

    $userID = $user->ID;
    wp_set_current_user( $userID, $username );
    wp_set_auth_cookie( $userID, true );
    echo 1;
    die();

}