How to close a doorway between two apartments?
First off, opening a common wall between two separate living units is fine if you occupy both units. It is however against most fire codes to have such a doorway between separate units. Now that you are selling one, you will need to reframe the opening and cover BOTH SIDES with the proper fire rated sheathing, ie: 5/8 or two 1/2 inch pieces of drywall.  

To do this, you should frame the opening with 2X4's on sides, top, and a center stud. Attach the drywall as you would for any other interior wall. Tape the seams and use joint compound to smooth the joints. Refinish/paint etc. This will restore the wall to it's original specification. Anything less than a proper fire rated repair should/would be picked up by a competent home inspector and will have to be repaired properly before you can close on the sale anyway. Good luck.