Cut three pieces of 1 by 4 inch lumber in 10 inch lengths. Use a quick square to mark the cut line on a perfect 90 degree angle. Use a circular saw or miter saw to make your cuts. These are your extension braces.
Set your braces on a level, sturdy surface on top of a scrap piece of lumber. Use a 1/8 inch wood bit to drill pilot holes in each of the three extension braces. Evenly space eight pilot holes across the face of each brace. Be sure the bit cuts all the way through the braces.
Mark the post on the three sides that the fence panel will not rest against five inches from the top. Use the quick square to mark the line at a true 90 degrees.
Place the first extension brace on one side of the post. Square up the edges of the extension with the edges of the post and the line. Drive a 1 5/8 inch treated deck screw through the lower four pilot holes in the extension brace. Place the next brace into place on the post and attach it in the same manner. Repeat the process with the remaining extension brace. You now have a 3½ by 3½ inch space directly on top of the post.
Cut a piece of 4 by 4 the length you need to make up the difference in the short post. Set it directly on top of the post surrounded by the three extension brackets. Drive screws through the extension braces into the new post brace.