By default, most versions of Outlook will move meeting emails from your inbox to the trash after you have chosen to accept the meeting.
However, you can prevent the meeting email from being moved to trash by changing the settings within the Options panel in Outlook.
The following step-by-step example shows how to do so.
Step 1: Open Outlook Options
In the top left corner of Outlook, click the File tab.
Then click the Options tab:

Step 2: Open the Mail Settings
An Outlook Options window will appear.
Click on the Mail tab:

Step 3: Change Default Settings
Next, scroll down to the section titled Send messages.
Then uncheck the box next to Delete meeting requests and notifications from Inbox after responding:

Once you click OK, your meeting emails will no longer be moved to the trash after you have accepted the meeting invite.
Instead, the email will simply remain in your inbox.
Feel free to use these exact steps to change the email settings in your own version of Outlook.
Related Tutorials
The following tutorials explain how to perform other common tasks in Outlook:
Outlook: How to Search Emails by Date Range
Outlook: How to Search for Attachment by File Name
Outlook: How to Export Emails to PDF
Outlook: How to Export Emails to CSV
