Clicking "Details" for an Activity History record which was generated from a "Completed" Activity should display both the core and any custom field values for that activity record.
This is handled by the following function:
We have the activity ID, so grabbing any associated custom_value records should not be a problem.
To recreate the "bug" - checkout this URL on demo:
(The underlying activity record - id=5 - has a custom field value for Volunteering hours which is not being displayed on the page).