Does the amount of heat absorbed as 1 kg of saturated liquid water boils to saturated vapor have to be equal to the amount of heat released when 1 kg saturated water vapor condenses at 100 degrees Celsius? Explain

Yes

Explanation:

The quantity of absorbed heat when one kilogram of liquid water which is saturated is boiled equals to the quantity of released heat when one kilogram of saturated water vapour condenses at 100 degree celcius because if they are not equal then some amount of excess energy can be created or can be destroyed from both the condensation and vapourization processes.

And this is a violation of thermodynamics first law.