In order to see the Transfer Employee/Change Post button and change employee posts, users need the permission 'Employee Posts', which can be added for them by their manager or any System Owner user by following the steps in our article on adding permissions.
Search for the employee and go to their profile.
Click the Security tab then click Permissions.
Click Edit Employee Permissions.
Search for Employee Posts.
Click the plus and pencil icons so they are not crossed out.
Click Save.