Migrate Import/Export Mappings
Assuming your location types and phone types etc have the same ids, you should just be able to copy over the two tables, mysqldump &lt;dbname&gt; civicrm_mapping civicrm_mapping_field &gt; somefile and then import the file into the other site's mysql database. But note that will **** OVERWRITE **** any mappings that you had already set up in the new site.

As noted in the comments there's some constraints so there's some extra steps:


If using mysqldump, use --skip-add-drop-table and --no-create-info. In phpmyadmin uncheck the option to drop/create tables.
In the new system do TRUNCATE TABLE civicrm_mapping_field then TRUNCATE TABLE civicrm_mapping.
Import civicrm_mapping first, then civicrm_mapping_field.