the relationship between these users must be examined.  Apparently, from the effect, it is unidirectional on edits

Log in as the A2E Service Account, open the A2E Console

Edit the relationship from the source user to the destination user who does not have the ability to edit.

These relationships are probably not bidirectional on edit, and may or may not be bidirectional on delete.  The edits are what we are after

Unidirectional means you cannot edit a copy of the item and then have it go back to edit the others

Open each relationship and change the settings

From

Conflict Resolution:       1 (Always Replace The Item In The Destination Folder)

Copied Resolution:        1 (Overwrite Changes)

 To

Conflict Resolution:       1 (Always Replace The Item In The Source Folder)

Copied Resolution:        1 (Sync changes back to source)

NOTE: if the relationship settings were set to

Conflict Resolution:       1 (Always Replace The Item In The Destination Folder)

Copied Resolution:        1 (Sync changes back to source)

this relationship settings will never allow the source item to update from the destination.  Change this relationship to the "Change To" desired settings above.

If one is wrong, chances are, many could be.  Check and update these settings for all relationships you want to be able to edit the destination and go back to source.

Then make a change to an item in the destination to test.

Then close the Add2Exchange Console and start the Add2Exchange Service to sync

The system will sync sync and you will be able to accomplish this for that user.

Check and edit any other relationships with this desired functionality.