Once they abolished slavery, adopted new state constitutions acceptable to Congress and ratified the 14th Amendment, they were readmitted to the Union.
This was all constitutionally questionable and went against the late Mr. Lincoln's understanding of the Constitution. In 1939, the Supreme Court refused to address it, admitting that in the heat of the moment, things were done that were not quite constitutional, but the Court didn't want to rip the scab off only 74 years after Appomattox.
Thank you for the information, I will look into it further.