Auto Populate timestamp during work item state transition
One answer
There is aging support available: https://jazz.net/library/article/1562 check if that is enough.
The best option is to use a Java Server extension as this can detect a state change easily. But it is expensive.
Another way you can try to implement this is a script based calculated value https://jazz.net/wiki/bin/view/Main/AttributeCustomization#Script_based_calculated_values . You can not really detect the state change very well here, but I think you can. Be dependent on the state look up the state and if the state is the desired one and the value of the custom timestamp is empty (whatever that means for a timestamp), copy the modified date over. It might be necessary to save again.