Legal Question in Real Estate Law in Georgia

The proper method of payment may have always been up to you, unless your paperwork required cashiers checks. You failed to tell us if it did, so there is no way to answer you as to what your papers say (you have them, we don't, and they mean what they say). (Landlords can decline to accept personal checks). In any event, unless you have a contract that SAYS he is to cover the cost of cashiers checks, you bear that cost, and CANNOT bill him.

You can send an invoice, and expect him to not pay or even respond. Just move to the new house, make sure you move from the apartment in good standing, then move on.