I think you can use cron-utils, which brings a CronBuilder class and allows to export to multiple formats. The feature is available from version 4.0.0 onwards.
An example from the README:
//Create a cron expression. CronMigrator will ensure you remain cron provider agnostic
import static com.cronutils.model.field.expression.FieldExpressionFactory.*;
Cron cron = CronBuilder.cron(CronDefinitionBuilder.instanceDefinitionFor(CronType.QUARTZ))
.withYear(always())
.withDoM(between(1, 3))
.withMonth(always())
.withDoW(questionMark())
.withHour(always())
.withMinute(always())
.withSecond(on(0))
.instance();
//Obtain the string expression
String cronAsString = cron.asString();//0 * * 1-3 * ? *
//Migrate to Unix format
cron = CronMapper.fromQuartzToUnix().map(cron);
cronAsString = cron.asString();//* * 1-3 * *
