'You can bet that rifle has long since disappeared!'
Hopefully not. If it was displayed in the Oval Office I'd think it was a high visibility item and would have been noticed if it went missing.
Those items received as gifts to the president are generally considered to be the property of the United States if they come from a foreign dignitary. Certain gifts are eligible for purchase by the president/first lady,
If received from a US citizen, they are generally considered to be the property of the president but will generally go into that president's library collection.
It could have been different when Kennedy was in office as the law was apparently substantially changed in 1966.
If similar procedures were observed when Kennedy was assassinated, the rifle would either be retained in the National Archives or would be at his presidential museum in its collections.
"The gift which I am sending you is called a dog, and is in fact the most precious and valuable possession of mankind" -Theodorus Gaza
Baby Jesus cries when the fat redneck doesn't have military-grade firepower.