Read receipt function is only available for the users who have hosted their email service with Google Apps and not available in personal Gmail accounts eg (user@gmail.com)
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A read receipt is an email notification delivered when a recipient opens (to read) an email you send. The receipt confirms that the recipient acknowledged your message and records the time.
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Below are the steps how the request will be sent:
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If you request a read receipt, request will be sent to every recipient in the To:and Cc: fields.
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- Compose a message as usual while using the desktop version of Gmail at mail.google.com.
- Click the More options icon in the compose window.

- Click Request read receipt.
- Send your message.
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Below are the steps how the request will be sent:
- Open and read the message as usual while using the desktop version of Gmail at mail.google.com.
- When you close the message or navigate away from it, you will be prompted to send a read receipt.

- Click Send receipts or Not now.
- If you click Not now, you will be prompted again the next time you open this conversation.
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Reference: https://support.google.com/mail/answer/1385059?hl=en