How is Ampere-hour calculated if four 65 Ah batteries in series for UPS?

The ampere-hour rating of series connected batteries is the same as that for one battery, so the ampere-hour rating of four 65 Ah batteries in series is still 65 Ah.

The reason for this is Kirchoff's current law - the signed sum of the currents entering a node is zero - or - the current at every point in a series circuit is the same.