Fix for Issue-13556 - Sorting in Product Listing via Quantity not work

app/code/Magento/CatalogInventory/Model/Source/Stock.php

@@ -26,4 +26,23 @@ public function getAllOptions()
             ['value' => \Magento\CatalogInventory\Model\Stock::STOCK_OUT_OF_STOCK, 'label' => __('Out of Stock')]
         ];
     }
+
+    /**
+     * Add Value Sort To Collection Select.
+     *
+     * @param \Magento\Eav\Model\Entity\Collection\AbstractCollection $collection
+     * @param string $dir
+     *
+     * @return $this
+     */
+    public function addValueSortToCollection($collection, $dir = \Magento\Framework\Data\Collection::SORT_ORDER_DESC)
+    {
+        $collection->getSelect()->joinLeft(
+            ['stock_item_table' => 'cataloginventory_stock_item'],
+            "e.entity_id=stock_item_table.product_id",
+            []
+        );
+        $collection->getSelect()->order("stock_item_table.qty $dir");
+        return $this;
+    }
 }

app/code/Magento/CatalogInventory/Test/Unit/Model/Source/StockTest.php

@@ -0,0 +1,44 @@
+<?php
+/**
+ * Copyright © Magento, Inc. All rights reserved.
+ * See COPYING.txt for license details.
+ */
+
+namespace Magento\CatalogInventory\Test\Unit\Model\Source;
+
+use PHPUnit\Framework\TestCase;
+
+class StockTest extends TestCase
+{
+    /**
+     * @var \Magento\CatalogInventory\Model\Source\Stock
+     */
+    private $model;
+
+    protected function setUp()
+    {
+        $this->model = new \Magento\CatalogInventory\Model\Source\Stock();
+    }
+
+    public function testAddValueSortToCollection()
+    {
+        $selectMock = $this->createMock(\Magento\Framework\DB\Select::class);
+        $collectionMock = $this->createMock(\Magento\Eav\Model\Entity\Collection\AbstractCollection::class);
+        $collectionMock->expects($this->atLeastOnce())->method('getSelect')->willReturn($selectMock);
+
+        $selectMock->expects($this->once())
+            ->method('joinLeft')
+            ->with(
+                ['stock_item_table' => 'cataloginventory_stock_item'],
+                "e.entity_id=stock_item_table.product_id",
+                []
+            )
+            ->willReturnSelf();
+        $selectMock->expects($this->once())
+            ->method('order')
+            ->with("stock_item_table.qty DESC")
+            ->willReturnSelf();
+
+        $this->model->addValueSortToCollection($collectionMock);
+    }
+}