Measure the inside groove in the back of the picture frame and cut a piece of 3/8-inch particle board to fit, using a table saw. Test fit the piece into the frame and sand the edges if necessary so that it fits easily, without forcing.
Roll out enough 1/8-inch-thick cork, available from hobby stores, to cover the front of the particle board panel. Use a square and a utility knife to cut the cork to fit the face of the panel.
Shake the can of spray glue for at least one minute. Position the particle board panel and cork on a sheet of newspaper to protect your work space. Point the nozzle of the spray glue at the particle board panel. Hold the can 8 to 10 inches from the surface. Apply a coat of adhesive, working in short, brush-like strokes, overlapping for adequate coverage.
Do the same for the back of the cork. Allow the adhesive to dry to the touch. Align one edge of the cork with the edge of the particle board. Roll the cork out onto the particle board, keeping the edges square. Press the cork into place as you go, smoothing it from the center out. Trim off any excess at the edge of the particle board with the utility knife.
Fit the particle board panel with the cork face turned to the front of the frame. Use wide masking tape around the edges of the panel to lock it in place. Screw 1/4-inch eye hooks into the back of the frame an inch down from the top corner and tie a length of 20-pound-test fishing line between the eye hooks for hanging.