In order for you to transfer CometChat from one location to another.
Please follow steps for the same & Verify.
Transfer 'cometchat' folder from 'old' location to 'new'. Do Changes in 'integration.php' as per your requirement. such as Database Credentials changes etc.
Copy All cometchat tables from the old database to the new database.
login to cometchat admin panel using your credentials.
Check your base URL Path from 'Settings->General'. If it's not correct please change it as per your requirement. Please refer below documentation for your reference.
Clear Cache from the left menu.
Clear Browser Cache.