I don't understand, the power cable that came w/ your PSU does not fit to the cord connection of your UPS so that you can power the UPS, or the power cable that came w/ your PSU does not fit to the cord connection of your UPS so the UPS can power your PSU? W/c is it? I don't think you even need a new UPS.
Will my UPS able to handle the PSU just at least for a minute to shutdown?
My UPS is 1500VA 850W
That will depend on your whole system power draw. If all your parts(whole pc + monitor if connected to UPS) will draw 850w greater than your UPS can handle then "no". How would you know how much your pc power(watts) draws, list all components you have so maybe I can help you again.