Business Use Case.
Lead, Contact, Account or Opportunity record owner is changed. Business wants to make sure that already assigned scheduled Tasks and Events are reassigned to a new record owner.
We need to create a Process builder to achieve this functionality.
1. Go to Setup --> Process Builder --> New. Select object you want this change to happen. Make sure to select "when a record is created or edited"
2. In step two specify the criteria. In this case Record Owned in Changed = True
3. Next select the Related Record Record.Tasks or Record.Events and specify which lookup need to change.
4. This is how final result looks. I am repeating the same Record Owner change process for both types of Activities - Tasks and Events.
Please note, record Owner will be only updated for Open Activities. All Activities from the past will remain with the old owner. What also makes sense.