Currently the Correspondence Tool in ACC doesn't contain much feature. Yes the idea of sharing the email with Project members or having the email thread in ACC, or creating one in ACC does seem useful. However, to properly handle the correspondence tool, the project require these email thread to be documented together either on the Project Closeout or Handover, or just documenting purposes. This was highlighted by the clients during the construction phase.
The only workaround that can be seen as usable is to go ahead on outlook and export the email thread from there. ACC should have this feature as well. Either exporting everything or individually.