Is it possible to give permissions on individual user inbox to anyother user who have same privileges. If we assigning tasks specific to the user instead of queue's.

There are two authentication mechanisms in place: one from LDAP and the other from an internal identity provider (IDP). A user exists in both LDAP and IDP. It is possible to grant access to the same Inbox for this user, since they have the same privileges in the system for both LDAP and IDP, and belong to the same person.

I think using static role you can give the permission to user.

Regards
Sadath