If the record is a "lead", there is "industry" field. However, if the record is a "contact", then there is no "industry" field. So once a lead is conerted to a "contact", the industry information is lost. How to have "industry" field in "contacts"?

Yes, you will see that when exported for sure. So here is how you create it:

1. Go to Setup | Customize | Contacts | Fields

2. Scroll down to Custom Fields and Relationships section

3. Click New

4. Select the Type as Formula

5. Label it as Industry

6. The Formula Return Type will be: TEXT

7. Formula:

   TEXT(Account.Industry)
   

8. Specify the Profiles that will need to see it

9. Choose if you want to display them on Page Layouts or not

10. Hit Save!