As a Freshchat user, here is how you can see all your previous conversations:
Go to the History tab under the Activity hub
Click on My conversations
If you are an owner, you will also be able to see your team's conversations under All chats.
If you are looking for a specific conversation, you can use the Filter option to filter out chats. You can filter by User, Type of chat (Conversation, Missed, Offline, Ignored) and Date range.