Substitutions of overdue tasks

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Hello everyone!
I've come across a problem today. One user has some tasks in one of the processes, some are a bit overdue, but that's planned (they keep some tasks active until they will be able to complete them). After setting up a substitution I found out that new tasks are assigned the way I expect - assignment for the user and his substitute. But the substitute has no access to the tasks that have been assigned to the user before setting up the substitution (I mean the active tasks). I had to do this manually. Is there a way to make substitutions work so that the substitute is being assigned even the overdue tasks?

EDIT: I came up with an idea to create action that gives the rights to the desired documents upon starting the substitiution.