Cream shortening and brown sugar in large mixer bowl until light and fluffy. Add egg, water and vanilla; beat well.
Combine whole wheat flour, baking soda and salt; stir into creamed mixture. Stir in oats and apricots.
Drop by rounded teaspoonfuls onto lightly greased cookie sheet; flatten slightly. Bake at 350 degrees for 10 to 12 minutes or until golden brown. Remove from cookie sheet and cool completely on wire rack.