3243408 - Cannot save dictionary item even user has Write access in Process Manager

User who has View, Write and Delete access cannot save the dictionary. 

You can check if the dictionary category's Publish Mode is set as "Automatically".

https://help.sap.com/docs/signavio-process-manager/workspace-admin-guide/add-custom-categories?locale=en-US#create-a-new-category

For dictionary items in those categories, user needs Publish right as well to save any update.

KBA , BPI-SIG-CA-SEC-UM-AM , Access Management for SAP Signavio , How To

SAP Signavio Process Manager all versions ; Signavio Process Manager all versions