function wpse_304392_login_by_id() {

    $user_id = $_POST['user_id'];

    $user = get_user_by( 'id', $user_id );
    if( $user ) {
        wp_set_current_user( $user_id, $user->user_login );
        wp_set_auth_cookie( $user_id );
        do_action( 'wp_login', $user->user_login );
    }

    wp_die(); //Essential for AJAX calls
}

function wpse_304392_login_by_username() {

    $username = $_POST['username'];
    $user = get_user_by( 'login', username );
    $user_id = $user->ID;

    if( $user ) {
        wp_set_current_user( $user_id, $username );
        wp_set_auth_cookie( $user_id );
        do_action( 'wp_login', $username );
    }

    wp_die(); //Essential for AJAX calls
}