Is it possible to move all constraint dates when moving data date?

When drafting a new programme, I will add constraint dates, so that float is shown for predecessors of the constrained activity only. However, when I move the project start date and/or data date, I have to manually change each constraint date by the same amount of time.

Is there a way to effectively lift and move the whole programme, including any constraint dates, so that the float remains unchanged?

There may be a very simple solution to this but sometimes when you use a tool for so long, you can lose the ability to see the obvious answer.

Thanks