The APC “Back-UPS RS-1500” UPS has an internal pair of batteries and a connector for an external pack to extend the runtime. The connector is (a) pretty big, and (b) not evidently something you can just go out and buy. Fortunately, I also had a totally dead identical UPS. The internal and external battery connectors are, mercifully, the same. So I just removed the dead built-in battery and snipped off the connector. There’s one on eBay right now for $15, so if you can’t get a second UPS then you could probably still get along.
The connector on the right is the one you need, the one on the left is what you’ll encounter on the back of the UPS.
From outside-edge-to-outside-edge, it’s 1.5 inches. The Molex part number is 870-1953A. That won’t match anything at Molex’s web site, or Newark for that matter. Google comes up dry… I suspect this is (semi-)custom for APC. The shape of the connector on the inside makes me think you could probably get away with 1/4″ spade lug connectors, but that makes me nervous thinking about it.
Anyway, paraphrasing John McClane, “Now I have the right connector. Ho ho ho!”