Along the sames lines as what Brady just commented.
We have had this happen a few times. The easiest solution is to move the tasks to the new project which brings all pertinent info with them. Updates, hours, etc. The downside is that if those hours or updates were at the project level, it will not carry over.
Although not ideal this would be another use case of the parent child project relationship. The child (proj b) would roll up to parent and could be marked complete.
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