Ideally, it's best that you create an export dump through phpmyadmin and export the tables over. Here's the general guideline that you could use and it is also what we used previously when we migrated from old site to new site.
NOTE:*Backup your data first before perform migration !important
NOTE:*Migrate all the old site user to new site first using 3rd party extension (make sure all the user id is same as old site)
1. Export all your EasySocial related table, that has prefix of #__social_*
NOTE: Please change the prefix #__ according to your database.
2. Download the exported tables .sql file and save it on your desktop.
3. Checks the database prefix for the new site. If the database prefix is the same with your old site/domain, you may skip this step. However, if the live site uses different database prefix, you'll need to edit the exported tables .sql file above and do a search and replace all database prefix accordingly.
4. Import your edited .sql file on steps 3, into your new site.
5. Then install latest EasySocial version on your new site.
NOTE:
You also have to migrate all your media files at JoomlaFolder/media/com_easysocial/.. (for photos, avatars, videos, comments, conversation attachments, links images and files.