Wash jars and lids in hot soapy water; rinse with warm water. Fill boiling-water canner half full with water; add jars and water to cover. Bring water to a boil, reduce heat and simmer. Place lids in water to cover in a small saucepan; bring water to a simmer. Simmer until ready to use. Remove and drain jars and lids, one at a time, as needed for filling.
Combine 4 quarts water and 1/2 cup lemon juice in a large bowl; set aside. Fill a Dutch oven 3/4 full with water; bring to a boil. Immerse apricots for 20 seconds or until skins easily peel away; remove with slotted spoon and plunge into ice water. Slip skin off apricots using a paring knife. Cut apricots in half; remove pits. Place in the lemon juice and water solution to prevent browning; drain. Place the apricots in food processor in batches; process until finely chopped. Measure exactly 6 cups of fruit.
Combine chopped apricots, 1/4 cup lemon juice, ginger, and pectin in a large Dutch oven; stirring until pectin dissolves. Let stand 10 minutes.
Bring mixture to a full rolling boil (a boil that doesn't stop bubbling when stirred) over medium-high heat. Boil 1 minute, stirring constantly. Remove from heat; add SPLENDA® Granulated Sweetener, stirring until SPLENDA® Granulated Sweetener dissolves. Skim off any foam with metal spoon.
Ladle hot preserves immediately into prepared jars, filling to within 1/4 inch of tops. Wipe jar rims and threads. Cover with 2-piece lids. Screw bands tightly. Place jars on rack in canner. (Water must cover jars by 1 to 2 inches. Add boiling water, if necessary.) Cover; bring water to gentle boil.
Process 10 minutes. Remove jars and place upright on towel to cool completely. After jars cool, check seals by pressing center of lid with finger. (If lid springs back, lid is not sealed and refrigeration is necessary.) Store in a cool, dark place for up to 1 year. Once opened, store refrigerated and use within 2 weeks.