When you frame the new wall, frame an opening for the window that is the same size that you want your finished window opening to be plus 2 times the thickness of whatever you plan on finishing the opening with. For example, if you want a finished opening that is 14" x 38" and you plan on using 1/2" drywall for your window box, frame the opening 15" x39". You will need blocking around the window to match the opening in the new wall. Use 2x material attached to the existing wall parallel to the opening in the new wall. Drywall or plywood will easily span the 8-10". If you use drywall, I'd look at mold-resistant for around the window.
Are you going to be installing casing around the opening in the new wall? If so, then using plywood for your window box is probably a better choice than the drywall.