Usually there's no need to take any special action. But to ensure the queries are using the new user's authentication credentials, you can follow these steps:

  1. Ensure new user has access to the Google Sheet
  2. Ensure new user has access to the data source accounts the query targets (for example, the AdWords accounts or Google Analytics views)
  3. Logged in to Google Drive as the new user, go to the file in question
  4. On the SupermetricsQueries sheet, delete the query IDs
  5. On the SupermetricsQueries sheet, on the very right there's a column marked "Refresh with user account". There you can mark the data source user account that should be used when refreshing the queries (eg. the Google Analytics login email address), if that is different than before.
  6. Using the Supermetrics add-on, refresh all queries

 This method will run the queries from scratch as new queries, using the authentication information of the current logged in user.