OK, as I see this, your telephone system has a battery back-up, not a UPS. That is to be expected in a large telephone PBX. DO NOT try and add anything to this system. It is designed specifically for the telephone system.
But, I also know that you may have a really large, cabinetised UPS that is designed to act like an emergency generator. These can be as large as a T&E room and can be sized for an entire building. The way to tell is if, what you are calling a UPS, is connected to a building breaker panel and not just a panel with 120 VAC outlets, then you have a free standing building UPS.
Patrick is correct. You should NOT mix telecom equipment with patient care equipment.
Having said all that, the fact that you have an emergency generator, simplifies this whole thing. If this is, indeed, a large UPS, just take a look at the rating of the breaker panel(s) that the system is connected to and do the calculations for VA size. Actually, a large system, like this, is rated in KVA as some are designed for hundreds of AMPS.
Rcaman