Quoted:
As a C&R FFL holder, when disposing a firearm to a non-licensee. Do I have to do a background check (Form 4473) on the non-licensee?

(f) Firearms receipt and disposition by licensed collectors.
(1) Each licensed collector shall enter into a record each receipt and disposition of firearms curios or relics. The record required by this paragraph shall be maintained in bound form under the format prescribed below. The purchase or other acquisition of a curio or relic shall, except as provided in paragraph (g) of this section, be recorded not later than the close of the next business day following the date of such purchase or other acquisition. The record shall show the date of receipt, the name and address or the name and license number of the person from whom received, the name of the manufacturer and importer (if any), the model, serial number, type, and the caliber or gauge of the firearm curio or relic. The sale or other disposition of a curio or relic shall be recorded by the licensed collector not later than 7 days following the date of such transaction. When such disposition is made to a licensee, the commercial record of the transaction shall be retained, until the transaction is recorded, separate from other commercial documents maintained by the licensee, and be readily available for inspection. The record shall show the date of the sale or other disposition of each firearm curio or relic, the name and address of the person to whom the firearm curio or relic is transferred, or the name and license number of the person to whom transferred if such person is a licensee, and the date of birth of the transferee if other than a licensee. In addition, the licensee shall cause the transferee, if other than a licensee, to be identified in any manner customarily used in commercial transactions (e.g., a driver's license), and note on the record the method used.

(2) The format required for the record of receipt and disposition of firearms by collectors is as follows:

Firearms Collectors Acquisition and Disposition Record

Description of firearm Receipt Disposition
Manufacturer and/or importer
Model
Serial No.
Type
Caliber or gauge
Date received
Name and address or name and license No.
Date of disposition
Name and address or name and license No.
Date of birth if non-licensee
Driver's license No. or other identification if non-licensee

Quoted:
Thanks! Really helpful.

In my state all firearms must be registered. Do I have to give the non-licensee a receipt or some kind of form of proof of purchase?

During firearm inspect for registration, you MUST have a receipt of where you got the firearm, and it must be registered within 3 days.