Adding "late" fee to an existing invoice

When does the late fee become payable? There is your answer.

The question was "HOW" not when.

You can manually create a new invoice or use the finance charge feature of the program or modify the inital invoice. The choice is up to you.

For a better audit trail, creation of a new invoice either manually or using the finance feature of the program is the preferable method used by professionals in the field.

You didn't understand your own question.

At some places policy has the late fee charged as of the original invoice date, so that it generates a larger finance charge the next month. [1] At other places policy is to charge the late fee on the late date.

Rather obvious that if the first applies you add it to the existing invoice, if the second, use the finance charge feature and generate a new invoice.

[1] A sneaky practice to make sure that the next's month bill is also late even if payment for the first bill arrives before the next one goes out as the customer doesn't know what the payoff amount with the finance charge is.