It's not possible to store the original format in WP and convert on output, otherwise you could just use the original table.
It needs to happen before insertion. The wp_insert_post() takes a WP_Post object as an argument. Thus you need to build this object using the various columns of the forum table as the data source, but all the object keys are pure WP. Translation will mainly be of the "assign this column value to this post key" nature. There could be some format conversions, perhaps the timestamps are different. One thing to watch out for is character mapping. Unless both tables use identical character maps, be sure the conversion is done correctly.