Is it possible to define different UOMs for invoices and orders?
Yes, it is possible. You can configure your invoicing unit at Products window, on Products tab. Then, you can add as much ordering units as you want on the units tab on the same window. Ordering units and invoicing unit can have a fixed relation or a flexible relation. You can define the fixed relation on the Units window. At every orders, shipments and invoices, you now can include two quantities, one for each unit of measure. The warehouse is registered with both units of measure.