How to connect a second battery to my UPS?
You can't switch your battery under load, that would lead to an inevitable voltage drop on the generated voltage keeping your devices working, and thus negate the idea of a UPS.

So, give your old battery into recycling, and only use the new one – even using both in parallel (if that was possible, which is not really the case) would be giving you but 25% more capacity than just the new one, so simply write off the old battery.