Combine pineapple and sugar in a large glass mixing bowl, stirring well. Cover and let stand 4 hours.
Place pineapple mixture in a flat-bottomed kettle; cook over low heat, stirring frequently, 30 minutes or until tender. Add strawberries, stirring well. Bring to a rolling boil; boil, stirring frequently, until mixture registers 220° on a candy thermometer or until mixture sheets from a cold metal spoon.
Quickly ladle conserve into hot sterilized jars, leaving 1/4- inch head space. Cover at once with metal lids, and screw bands tight. Process in boiling water bath 15 minutes.