Get an image from url in front end submission form

You have not created the attachment as link to the post, you will need to do that first. Then you can use in the content.
Alternative it is possibel to upload to other path, but better is a link in the post, post-ID to attachment-ID.

Easiest way to do that is with wp_insert_attachment(). This function takes an array of a few parameters, the filename (the file must already be in the proper uploads directory), and the post ID of the parent post that you want to attach the attachment to.

You find different answers here for this topic; like 40301

Edit #1:

At first the field for th upload in form for the follow example:
<input type="file" name="files[]" multiple>

And now the workflow for upload the attachments:

    // Only for outside WP Theme; if you have this in a file you will need to load "wp-load.php" to get access to WP functions.  If you post to "self" with this code then WordPress is by default loaded
    require $_SERVER['DOCUMENT_ROOT'] . "/wp-load.php";
    // require two files that are included in the wp-admin but not on the front end.  These give you access to some special functions below.
    require $_SERVER['DOCUMENT_ROOT'] . "/wp-admin/includes/file.php";
    require $_SERVER['DOCUMENT_ROOT'] . "/wp-admin/includes/image.php";

    // required for wp_handle_upload() to upload the file
    $upload_overrides = array( 'test_form' => FALSE );

    global $current_user;
    get_currentuserinfo();
    $logged_in_user = $current_user->ID;

    // count how many files were uploaded
    $count_files = count( $_FILES['files'] );

    // load up a variable with the upload direcotry
    $uploads = wp_upload_dir();

    // foreach file uploaded do the upload
    foreach ( range( 0, $count_files ) as $i ) {

        // create an array of the $_FILES for each file
        $file_array = array(
            'name'     => $_FILES['files']['name'][$i],
            'type'     => $_FILES['files']['type'][$i],
            'tmp_name' => $_FILES['files']['tmp_name'][$i],
            'error'    => $_FILES['files']['error'][$i],
            'size'     => $_FILES['files']['size'][$i],
        );

        // check to see if the file name is not empty
        if ( !empty( $file_array['name'] ) ) {

            // upload the file to the server
            $uploaded_file = wp_handle_upload( $file_array, $upload_overrides );

            // checks the file type and stores in in a variable
            $wp_filetype = wp_check_filetype( basename( $uploaded_file['file'] ), null );   

            // set up the array of arguments for "wp_insert_post();"
            $attachment = array(
                'post_mime_type' => $wp_filetype['type'],
                'post_title'     => preg_replace('/\.[^.]+$/', '', basename( $uploaded_file['file'] ) ),
                'post_content'   => '',
                'post_author'    => $logged_in_user, // or use a static ID
                'post_status'    => 'inherit',
                'post_type'      => 'attachment',
                'post_parent'    => $_POST['post_id'],
                'guid'           => $uploads['baseurl'] . "https://wordpress.stackexchange.com/" . $file_array['name']
            );

            // insert the attachment post type and get the ID
            $attachment_id = wp_insert_post( $attachment );

            // generate the attachment metadata
            $attach_data = wp_generate_attachment_metadata( $attachment_id, $uploaded_file['file'] );

            // update the attachment metadata
            wp_update_attachment_metadata( $attachment_id, $attach_data );

                    // this is optional and only if you want to.  it is here for reference only.
                    // you could set up a separate form to give a specific user the ability to change the post thumbnail
                    // set_post_thumbnail( $_POST['post_id', $attachment_id );
        }
    }