To grant a customer a free month, two steps are necessary. First you have to create a 100% discount, which is unlocked for the plan variant of the customer.
To create a discount go to "Products > Discounts > Create Discount". Create the discount as follows:
Then go to the customer's contract details (Customer > Contract ID) and click "Perform Action > Up-/Downgrade". Select no(!) plan and no plan variant, set the date to "Next Billing Date" and add the discount. In addition, you can check the "Inherite Start Date" option to retain the original contract and cancellation periods. Then click "OK" and the discount is booked for the next month:
The contract details now look like this: