In order for you to transfer CometChat from one location to another.
Please follow steps for the same & Verify.
Step 1:
Transfer 'cometchat' folder from 'old' location to 'new'. Do Changes in 'integration.php' as per your requirement. such as Database Credentials changes etc.
Step 2:
Copy All cometchat tables from the old database to the new database.
Step 3:
login to cometchat admin panel using your credentials.
Step 4:
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.
https://kb.cometchat.com/hc/en-us/articles/360000002756-How-to-change-Base-URL-
Step 5:
Clear Cache from the left menu.
Step 6:
Clear Browser Cache.