@Laura Huico For a bot created using bot framework you need to enable storage of the conversations to a database like cosmos DB or blob storage to get the chat conversation history. The official documentation details steps to create this configuration for a bot. This is basically creating a app settings file with the details of your storage and referencing then in the bot to store the conversation data.
Since you have used the composer to create the bot it might have a memory system to store some information about your chat like user profile, information, session data etc, but saving entire chat conversations might be limited at this point of time. A recent thread on how you can use blob storage for basic conversation scenarios is detailed in the thread but scenarios like handover to humans might still need custom code or you can configure cosmos DB and store the data in DB as mentioned by the user in the thread. I hope this helps.