As the system default, "assignee" and "system administrator" can close the opportunity.

Under normal circumstances (except for cases where role permissions have been setup manually), although the "business representative" of a opportunity can add, edit, and delete opportunity data, it does not have the authority to close the opportunity.

Therefore, if you want the business representative to control the function of closing the business opportunity, you can set the representative as the "assignee" of the opportunity data.


Note: How can I assign someone responsible (assignee) for certain data?