Measure the height of the existing fence posts and determine how much higher you want to raise them. Count the number of posts running along the fence line so you know how many lengths you need.
Position an end of a metal tie plate over the end of the extension post that you will join to the existing post. Insert six 1 1/4-inch galvanized screws through the holes in the plate that penetrates the extension post. Repeat the process of attaching another identical plate to the other side of the extension post, so the protruding ends of both plates are parallel to each other.
Stand the extension post firmly over the top of the current post. Insert 6 screws to join the end of each metal plate to the current post, thereby joining the extension post to it. Repeat the process of attaching post extensions to the remaining posts.
Cut the lattice sheet to the desired height and width using a table saw. Measure the width of the wood panels between adjacent posts so you cut the lattice to the required width.
Construct a frame using two horizontal and two vertical lengths of 2-inch by 2-inch lumber for each lattice panel. Measure the length and width of the panel and cut horizontal and vertical boards to match it. Bevel the edges of the frames at 45 degrees using a miter saw.
Form a groove along one side of each 2-by-2 using a router saw so the panel fits inside. Insert one edge of the lattice into one grooved 2-by-2 at a time, pushing and pulling to form a secure and snug fit.
Drill two pilot holes through the corners of each long frame board and one through the corner of each short side. Drive a 2-inch galvanized deck screw into each hole to hold the corner together.
Paint or stain the lattice panel and leave it to dry. Position the panel between two post extensions and check its plumb with a level. Drill a row of 3-inch deck screws to join the side frames of the panel to the posts.