It's the 'migration' that most of SIers hate. Customers of Questetra often ask question about it.
However...
In the first place, "the date of processed" of each Tasks is that important. It doesn't make much sense to move "business data" as final deliverable alone. No, rather you shouldn't move 'business data' at all... (Whoops, I shouldn't be curt that way. Some people want solution seriously.)
If you do want to migrate "business data" in your workflow to your new system, you've got to do is to setup a 'data spout'. For a concrete example, I will show you a process model in my latest article "Learn BPMN by 'Daily Report'". The workflow definition (Workflow Diagram) below looks like the same as the one before at a glance. But there added one strange Start point.
[Daily Report flow - Record Tasks]
It becomes to bit technical but, the added start point (BPMN icon) , is called 'Message Start Event'. 'Message Start Event' is used for connecting Workflow to another Workflow.
Adding such 'Message Start Event' at near the End point of a business process (Workflow), pouring business data of the past into it by "REST" access, then each business data will reach to the End point of the Workflow while no one sees. That is, business data without "date of each Task processed" will be stored. Incidentally, although somebody must do programing 'an external program for pouring into', I guess you could beg to do 'a day's work' to a Web-based engineer.
[Daily Report flow - Record Tasks : [2. Comments to the Report] screen]
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