2S BMS for Li-ion Battery not charging the batteries
The BMS you linked doesn't look to include a battery charger. And that's true with most BMS circuits you find online. The purpose of this board is more to protect against Over Charge, Over Discharge, and Over Current. So for your project, you'll either need to buy some type of charger board that works with your UPS, or you'll have to design one.
Also, I would encourage you to either find a BMS that has balance charging for the cells, or use some type of battery management IC for balance charging. Cause I don't think the BMS you included has that feature either.