Currently, Senta does not have a dedicated field to store the outgoing text messages, however you can create a workaround via the Add note feature on the text messaging task.
Firstly, you will need to copy the the contents of the text message. To do this, select Send the text message:
Copy the contents of the message and return to the job by selecting Cancel:
To add a note to the text message task, select Add note:
This will take you to the Add new task note modal where you can paste the copied text message:
Once you save the changes, the note will be added to the text message task. You will be able to view this even after the task has been completed: