Switch E-Mail Conversation off after Chat

Hello Judith,

I hope all is well! The customer will only receive an email if you are proactively sending an email or if you have set up notifications sent via business rules such as Triggers and Automations. If that is the case, you can exclude the chat channel from those business rules, but be careful not to change those triggers that operate to send the message to the customers, such as Zendesk default triggers that notify the requester, for example, otherwise you can have issues when you actually decide to change the communication channel. You can read more about email operation here. 

I hope it helps!