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Oregon does not require license or registration of a firearm. The only time that license is required is if you want to carry it concealed.
So normally if there is some type of temporarily transfer such as for hunting or target shooting no written document is needed. However, if one individual gives another individual a gun lets say for protection there should be a bill of sale (if only for $1) or the ownership can be transferred through any gun shop.
Here are some of the laws that someone who wants to transfer a gun has to adhere to, and if they don't they can be charged with a crime:
It is unlawful to sell, deliver, or transfer any firearm to: