Then open SharePoint Designer, open the list, create new workflow.
Create an impersonation step (Note: this step will run using the credentials you opened the SharePoint site with)
The following workflow is an example from some work I did, where we assign full control to only the assigned to person (or group). I had to also add an additional step to also assign full control to another group (ADMIN), as the workflow would crash if I allowed multiple selection of groups/users for my assigned to column.
Let’s go through each step.
Set a variable equal to the Assigned to field for the current task list item
REPLACE the current task list item rights to Full Control for current Assigned To user/group. Notice we used replace, this is important.
Then add same rights(as in B) for the ADMIN group, this is to ensure that we also have a group that we can put users into that can see everyone’s tasks.
Save the workflow, publish. Make sure you’ve set the start workflow on item create and change. So when task is created, rights are assigned, also when task is changed, as assigned to may be changed, so we need to update the task.