Arrange peaches around the bottom inner sides of clean rubber-seal jars. Fill jars with enough raisins to press peaches firmly against sides. Repeat procedure, alternating prunes, figs, and apricots in place of peaches, until jars are filled with fruit.
Pour rum over fruit in each jar, leaving 1/2-inch head space. Place rubber seal on rim of each jar. Secure glass lids firmly over seals by clamping metal clasps. Store at room temperature 3 weeks.