Create a new FAL element in TCA. To use it, change the current field name "new_fal_image" and the table name "YOUR TABLE NAME", so that TYPO3 find your image

ext_tables.sql

CREATE TABLE your_table_name (
  new_fal_image int(11) DEFAULT '0' NOT NULL,
);

TCA_FAL.php

'columns' => array(
  'new_fal_image' => array(
      'exclude' => 1,
      'l10n_mode' => 'mergeIfNotBlank',
      'label' => 'FAL image label',
      'config' => \TYPO3\CMS\Core\Utility\ExtensionManagementUtility::getFileFieldTCAConfig(
          'media',
          array(
              'appearance' => array(
                  'showPossibleLocalizationRecords' => 1,
                  'showRemovedLocalizationRecords' => 1,
                  'showAllLocalizationLink' => 1,
                  'showSynchronizationLink' => 1,
              ),
              'foreign_match_fields' => array(
                  'fieldname' => 'new_fal_image',
                  'tablenames' => 'YOUR TABLE NAME',
                  'table_local' => 'sys_file',
              ),
              // custom configuration for displaying fields in the overlay/reference table
              // to use the newsPalette and imageoverlayPalette instead of the basicoverlayPalette
              'foreign_types' => array(
                  '0' => array(
                      'showitem' => '
			--palette--;LLL:EXT:lang/locallang_tca.xlf:sys_file_reference.imageoverlayPalette;imagePalette,
			--palette--;;imageoverlayPalette,
			--palette--;;filePalette',
                  ),
                  \TYPO3\CMS\Core\Resource\File::FILETYPE_IMAGE => array(
                      'showitem' => '
			--palette--;LLL:EXT:lang/locallang_tca.xlf:sys_file_reference.imageoverlayPalette;imagePalette,
			--palette--;;imageoverlayPalette,
			--palette--;;filePalette',
                  ),
              ),
          ),
          'jpg,jpeg,gif,png'
      ),
  ),
),