Symptoms
The staff member is assigned a role with the privileges that seem to be enough for order placement (ORDERS_VIEW, ORDERS_CREATE, ORDERS_PROCESS), but button "Add New Order" is missing on the related screens.
Cause
The issue is caused by the bug with id #PBA-67320 ("Not possible to place orders without ACCOUNTS_CREATE_MODIFY").
Resolution
The bug is to be fixed in one of the upcoming BA updates.