Original Lincoln

What happened to the Lincoln Continental limo JFK was riding in when he was shot?
I have heard half a dozen different stories as to what became of the Lincoln Continental limo JFK was riding in when he was shot. I heard LBJ had the car pulled from service and destroyed. I also heard it was put back into service, as well as another yarn that it was stolen. One account suggests it is in a private collection while another suggests the car is in a museum.
What’s the real story? If by chance its in a real museum- what percentage of it is original, datring back to Nv 1963? The rumor regarding it being in a museum also suggests the car was gutted, rebuilt and repainted.
If it is in a museum- which museum?
I saw the car in the Henry Ford Museum in Michigan in 1988,but don’t know if it is still there. I can’t see anyone destroying a piece of history such as that.
The same museum also had the chair that Lincoln was sitting in when he was killed. I think it was on loan from another museum at the time.
Freestyle Folklore: The Grand Adventures of Abraham Lincoln