To convert all questions and categories from the free/trial version to the purchase version, basically all you need to do is rename all the tables in phpMyAdmin from jos_bfquiztrial to jos_bfquiz etc, and update the categories.

The following SQL commands should help.

RENAME TABLE `jos_bfquiztrial` TO `jos_bfquiz`;

RENAME TABLE `jos_bfquiztrial_matrix` TO `jos_bfquiz_matrix`;

RENAME TABLE `jos_bfquiztrial_scorerange` TO `jos_bfquiz_scorerange`;

RENAME TABLE `jos_bfquiztrial_37` TO `jos_bfquiz_37`; (where 37 is your category id number, repeat for all categories)

UPDATE `jos_categories` set `section` = 'com_bfquiz' where `section` = 'com_bfquiztrial';