In Rules & Triggers, for any inbound message you receive, you can forward that reply to your email address (or email addresses).
How do you set it up?
This depends if you want to send replies of campaigns to your email or have all general inbound messages sent to your email.
The main difference being that if If you are looking to manage all general inbound messages, then you'll have to get a dedicated number.
After you do that, go to Settings > Rules & Triggers.
Create a rule for RECEIVING SMS.
Select if the rule will be triggered when a messages is sent to any number, a shared number or one of your dedicated numbers (if applicable) based on which messages you want to receive.
Leave the keywords boxes empty and click NEXT.
When choosing the actions, select Forward to Email(s).
Once you are finished, click SAVE RULE and your incoming SMS will be forwarded to the assigned email addresses!