Final answer:
The statement is false; the Border States were resistant to Lincoln's proposals for emancipation and the adoption of the Thirteenth Amendment was contentious.
Step-by-step explanation:
The statement that the Border States quickly accepted President Abraham Lincoln's proposals for gradual compensated emancipation and willingly implemented the Thirteenth Amendment is FALSE.
The reality was quite complex. The Border States initially resisted Lincoln's proposals for emancipation, especially the idea of compensated emancipation because it implied an eventual end to the institution of slavery, which they wanted to preserve.
Additionally, the Thirteenth Amendment, which formally abolished slavery throughout the United States, was passed by Congress late in the Civil War, and ratification by the states was a contentious process.