There are 2 ways of fulfilling this project. The first way: embroider all three parts on wash-away stabilizer. Rinse the stabilizer, air-dry the embroidery, iron it.
Glue to a piece of cardboard.
Cut out a mat and frame the embroidery.
The second way is to use fabric. Embroider all three parts on separate pieces of fabric, skipping the first file from every part. Stitch all three parts, leaving about 3/8 inches between the parts. Cover the seams with a bias tape. Machine-stitch one side, then slip-stitch the other side of the tape.
Mount the embroidery on the cardboad. Cut out a mat. The mat should match the color of the bias tape.