If one of your users does not see the Dedupe tool in Apsona, here are a few things to check:
NOTE: As a first step, Always ask users to clear their Apsona cache if they have access issues. If the issue persists,then look at these things:
Make sure the user has been assigned a license. Go to Setup | Installed Packages, and click Manage Licenses next to the Apsona Dedupe and Match package.
User's profile (or perm set) must have create, read, edit, delete access to custom object "Dedup Data"
User's profile (or perm set) must have the "Dedup Enabled" checkbox checked on the custom object "Apsona Items"
User's profile (or perm set) must have create, read, edit, delete on the object they will de deduping. This is because they need to edit and delete records that other users will own, which is restricted by default in Salesforce. Depending on the "org-wide defaults" settings, user may need "modify all" access on the object so that they can dedupe records that are owned by other users.
See this article for additional detail.