It is not possible to capture the history of task update data and copy it to another project. You would need to do it manually - accepting the fact that the entry date would be different (if that mattered).
By manual I mean making a template of the project and then updating that template as if you were the user(s) updating the tasks by creating an entry for each task work entry from the original project.
Could be easy if there are few users, few updates and few tasks. Could be daunting if you have a lot of those things. What's the purpose of copying the data over? Are you looking for all task/task data to be copied or just portions? Was the time entered in the wrong project or something? Maybe there's another way around copying.