In a blender, combine strawberries, sugar, freeze-dried strawberry powder (if using), lemon juice, and salt, and process until very smooth, about 30 seconds.
Pour purée into a medium bowl, add jam, and whisk until thoroughly combined.
Divide evenly between six 3-fluid-ounce popsicle molds and freeze until solid, at least 8 hours (to make filling the molds easier, you can transfer the puréed strawberry base back to the blender jar or to a measuring cup or another vessel with a spout first). To unmold, follow your popsicle mold's instructions.