Invoice Units of Measure

Hi

We want to know how we can create the invoice where the invoice UOM different than in purchase order? We have one supplier that we need to raise the purchase order in BOX UOM and price is also in BOX, however, when they send the invoice, they will send it in LBS UOM and price is also in LBS.

We don't have the inventory configured. We want to check following things:

1. Can we create the UOM conversion without inventory configured? 

2. If we can create UOM Conversion without inventory, do we need to define the conversion rate between UOM? because supplier also can't inform us the exact conversion rate between UOM, for example, for chicken, when we order 2 boxes, the price of each boxes is 10 USD, but when supplier send the invoice they charge us based on weight of the chicken in each boxes. So the weight can vary, for example, sometimes 1 Box can be equal to 1.2 LBS and sometimes 1 Box can be equal to 1.3 LBS and so on.