Permission error when trying to link work item as parent to a task in same project area
One answer
The question lacks a lot of details, which is a shame.
I wonder why there is the emphasis on "the same project area". Just because one has access to some data in a project area does not necessarily mean that they have access to everything.
The error mentions the "permission to read item". This could indicate that there is an access permission enforced in the project area. This can either be based on work item categories and team areas, or this can be done manually by making the Access Context accessible as attribute.
I would suggest to ask the user to try to open the work item in question. If they can not you probably have read access limitations enabled and this is the desired behavior. The user would have to ask someone with access to the parent to do the change.
You can see that this is enabled in the process configuration, either the categories, or in the editor presentation making the access context attribute available for editing.
IF not, I would suggest to open a case with support, to find out what is going on.