Preheat oven to 350 degrees F (175 degrees C). Grease cookie sheets or use parchment paper.
In a medium bowl, cream together the 1/2 cup shortening, cream cheese and milk until well blended. Stir in the brown sugar and 1/4 cup of apricot preserves. Combine the flour, baking powder, cinnamon and salt; stir into the batter. Mix in the pecans last. Drop by rounded spoonfuls onto the prepared cookie sheet. Cookies should be about 2 inches apart.
Bake for 8 to 10 minutes in the preheated oven. Allow cookies to cool on baking sheet for 5 minutes before removing to a wire rack to cool completely.
To make the frosting, combine the confectioners' sugar, remaining apricot preserves and 1 tablespoon shortening; mix well. Frost cooled cookies and sprinkle with coconut if desired.
