It is true, a completed task cannot be modified with workflow. For some custom billing functionality, we needed to modify an attribute on a task, after it had been completed. Although I knew workflow could not modify it, I thought I had read where a plug in can handle this with no problem. Well, no, a plug in cannot modify a completed task either. What were we to do? 

 

 
A coworker, who can’t stand to be told “it cannot be done”, found a solution for us… using workflow! Although it is true a completed task cannot be modified, we can temporarily change the status of the completed task, make the change, then change the status back to completed. Voila! We have now modified our completed task and our processes can continue as spec’d out. 
 
Here’s what the workflow might look like:

Modify_Completed_Microsoft_CRM_Activity

Thank you Michael!