To check sent emails and messages in Odoo, you can follow these steps:

Open your Odoo account and go to the "Messaging" app.
Click on the "Inbox" button at the top left corner of the page.
On the left-hand side menu, click on "Sent".
Here, you will see a list of all the messages and emails you have sent from your Odoo account, along with their status and recipient information.
You can filter your sent messages based on various criteria such as date, recipient, status, etc.
Click on any sent message to view its details such as the message body, attachments, etc.

Greetings,
Peter