Use 'getParser' rathe than name the parser

CRM/Contact/Import/Form/Preview.php

@@ -245,9 +245,11 @@ class CRM_Contact_Import_Form_Preview extends CRM_Import_Form_Preview {
    * @return \CRM_Contact_Import_Parser_Contact
    */
   protected function getParser(): CRM_Contact_Import_Parser_Contact {
-    $parser = new CRM_Contact_Import_Parser_Contact();
-    $parser->setUserJobID($this->getUserJobID());
-    return $parser;
+    if (!$this->parser) {
+      $this->parser = new CRM_Contact_Import_Parser_Contact();
+      $this->parser->setUserJobID($this->getUserJobID());
+    }
+    return $this->parser;
   }
 
 }

CRM/Import/Forms.php

@@ -579,8 +579,7 @@ class CRM_Import_Forms extends CRM_Core_Form {
    */
   protected function getMappedFieldLabels(): array {
     $mapper = [];
-    $parser = new CRM_Contact_Import_Parser_Contact();
-    $parser->setUserJobID($this->getUserJobID());
+    $parser = $this->getParser();
     foreach ($this->getSubmittedValue('mapper') as $columnNumber => $mappedField) {
       $mapper[$columnNumber] = $parser->getMappedFieldLabel($parser->getMappingFieldFromMapperInput($mappedField, 0, $columnNumber));
     }