Hi Lila,
I suspect the closest you could get would be to create a Task report that (using Handoff Date, Predecessors, and EXISTS) would present "Task 1 on Project A" to the viewer (ideally, along-side the now-complete "Last Task on Project B") so that the user could then easily manually mark it as complete (with the same Last Task on Project B Actual Completion Date, for consistency).
If that's too much work (or happens too frequently), you could automate it using Fusion or our UberCalc solution.
Regards,
Doug