if your UPS has a good battery, but the device is still showing no battery installed, this video might help.

The Omron relays discussed in this video are model # G2R-14-T155. Their customer support was very helpful in responses to me. In short, the T155 indicates a temperature threshold of 155C. This part is not readily available in the US market, and would require some vendor/company to order them for resale here. It was suggested to consider the G2R-14-T130 (with a lower insulation class rating of 130C) as a possible replacement part.

Should I ever need to replace one of these relays, I will go this route and post a follow-up video. However, at $6-7 each, if more than one or two are faulty in your UPS, it may be cheaper to replace the whole unit with good used one.