Read this AEM Doc:
Looks like you can control various workflow permissions by using CRXDE lite:
For your use case - place the author in a group and then give that group the same permissions for a given workflow as the admin has. That should let the user see messages in the inbox.
Adding to what Scott has mentioned, Workflow models inherit a default access control list (ACL) for controlling how users can interact with workflows. To customize user access for a workflow, modify the Access Control List (ACL) for the workflow model node in the repository.
The following example restricts content authors from starting a workflow called mymodel. To restrict access, the Authors group is denied read access to the /etc/workflows/models/mymodel node.
The following diagram shows the default ACL for mymodel (the default ACL for all new models). The Authors group is a member of the contributor group, so Authors are allowed the jcr:read privilege for the node.
Read full article at :- https://docs.adobe.com/docs/en/cq/5-6-1/workflows/wf-admin.html
I hope this will help you.
Thanks and Regards