How did president lincoln succeed in permanently abolishing the practice represented by the tree in this cartoon ?

The 13th Amendment was enacted to abolish Slavery in all its forms. It was endorsed by the Senate on 8th of April 1864, and by the House on 31st of January, 1865. As soon as the House ratified it on February 1st 1865, Abraham Lincoln ratified the Joint Resolution of Congress and forwarded the the proposed amendment to the state legislatures where the required number of states gave their consent on the 6th of December, 1865.