Nia,
Are you trying to link just a Purchase Invoice or was the Purchase Invoice for a Purchase Order that was drop shipped to a Customer? The Purchase Invoice itself has no link directly to the Customer table to make reference. You could use the Shipping Tab/Custom Address field and type the Customer it was affiliated with.
As Suresh noted, on the Purchase Order you can link Customers to Purchase Orders on the Shipping Fast Tab.

Also note that Drop Shipments will automatically link Purchase Orders to Sales Orders.
Hope this helps.
Thanks,
Steve