Assuming you have already created your Text Message Survey and now would like to map the responses from participants to subscriber fields.
Step 1: Go to Manage Campaigns -> Select your Survey Campaign
Step 2: Go to Advanced settings in your survey campaign,
Step 3: Check the subscriber profile Campaign checkbox as shown in the picture
and click save.
Step 4: Go back to your campaign and Go to Manage questions -->click Edit question
Step 5: You will find subscriber field mapping drop down, where you will have all subscriber fields along with custom fields to which you want to map the user response to that question. select the field you want to map.
Click update to save the changes.
When users replies to your survey questions you will find the responses in the fields you mapped in detailed survey report and also in manage subscribers.
Note: You can use mapping fields option to both free text survey questions and Multiple choice questions.