6 months is too long. There are many invoice frauds out there. Its not uncommon for a company to receive invoices for stuff they never ordered or get double invoiced. Suddenly getting an invoice 6 months after you think accounts are all settled is unsettling and reputation damaging. I wouldn't expect to get paid, or get more work. Are you thinking like an employee or a business owner?
Personally I would say Not To Invoice--after 6 mos. and a record keeping / processing error on your part. True, the tone of his reply was harsh, however, you could expect the majority of tones to be harsh in this situation most of the the time. I know if I got an invoice MOS. later from anybody it would be a little disturbing so the fiesty attitude could be understood.
The only other thing I'd weigh is whehter or not you expected any future benefit /work could come from this relationship? If it could you'd almost for sure kill that after this invoice... if not, I might (an exceptionally tenative might) pursue it. On second thought, drop it and roll in into the "@##@%#@% I better keep better more timely records myself next time" category.